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The Adinkra Guide: Downloadable Resource

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The Adinkra Guide: Downloadable Resource

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This resource contains a collection of symbols I use as well as some of my artwork. Hundreds of adinkra are not mentioned here, so I hope you take the time to learn more about adinkra in your free time and maybe create your own art!

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Revised: June 18, 2022

I discovered adinkra before I knew of its meaning or relevance in African society. Many years ago my mother purchased a handful of adinkra stamps from Ghana. They lived in the basement of our home for years until one day she suggested I do something with them. That is when I began using a few of the stamps on clothing items. That is where Tribal immunity was born. Since then, I have become an independent researcher, learning about different symbols when I could and growing more interested over time.

My introduction to adinkra is not unlike many Diasporan Africans, as we find joy in learning about our ancestral histories. We see these histories in the iron and stone mason work of buildings and homes throughout the Americas and Caribbean. Adinkra no longer only belongs to the Akan of West Africa, it belongs to all of Africa’s children willing to connect with an unerasable past.

My favorite go-to resources include: adinkra.org and, my personal favorite, The Adinkra Dictionary, but as adinkra has grown in popularity over the years, more resources have been made available online and through new publications.

This resource contains a collection of symbols I use as well as some of my artwork. Hundreds of adinkra are not mentioned here, so I hope you take the time to learn more about adinkra in your free time and maybe create your own art!

Looking for an adinkra handbag by Tribal Immunity? Click here,

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The Adinkra Guide: Downloadable Resource

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Revised: June 18, 2022 I discovered adinkra before I knew of its meaning or relevance in African society. Many years ago my mother purchased a handful of adinkra stamps from Ghana. They lived in the basement of our home for years until one day she suggested I do something with them. That is when I b…

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In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. You will learn how to perform the transformations, and how to map one figure into another using these transformations.

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The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

the 2 is found by adding the two numbers before it (1+1),

the 3 is found by adding the two numbers before it (1+2),

the 5 is (2+3),

and so on!

Example: the next number in the sequence above is 21+34 = 55

It is that simple!

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ...
Can you figure out the next few numbers?
Makes A Spiral

When we make squares with those widths, we get a nice spiral:

Do you see how the squares fit neatly together?
For example 5 and 8 make 13, 8 and 13 make 21, and so on.

This spiral is found in nature!
See: Nature, The Golden Ratio, and Fibonacci

The Rule

The Fibonacci Sequence can be written as a "Rule" (see Sequences and Series).

First, the terms are numbered from 0 onwards like this:

So term number 6 is called (which equals 8).

x
₈ = x ₇ + x ₆

So we can write the rule:

The Rule is xn = xn−1 + xn−2

where:

Example: term 9 is calculated like this:

Golden Ratio

And here is a surprise. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio " φ" which is approximately 1.618034...

In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:

We don't have to start with 2 and 3, here I randomly chose 192 and 16 (and got the sequence 192, 16,208,224,432,656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ...):

It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this!

Using The Golden Ratio to Calculate Fibonacci Numbers

And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio:

The answer comes out as a whole number, exactly equal to the addition of the previous two terms.

When I used a calculator on this (only entering the Golden Ratio to 6 decimal places) I got the answer 8.00000033 , a more accurate calculation would be closer to 8.

Try n=12 and see what you get.

You can also calculate a Fibonacci Number by multiplying the previous Fibonacci Number by the Golden Ratio and then rounding (works for numbers above 1):

Example: What is the next in the sequence after 8 ?

It will be 8 times φ:

Some Interesting Things

An odd fact:

Why?

Because adding two odd numbers produces an even number, but adding even and odd (in any order) produces an odd number.

Lucas Numbers

Starting the sequence with 2 and 1 we get the "Lucas Numbers". They get closer and closer to the powers ( exponents) of the Golden Ratio:

For example, the 15th Lucas Number is approximately φ ¹⁵ = 1364.0007..., so is exactly 1364. Try it yourself!

Here is the Fibonacci sequence again:

There is an interesting pattern:

Look at the number . Every 3rd number is a multiple of 2 (2, 8, 34,144,610, ...)

Look at the number . Every 4th number is a multiple of 3 (3, 21,144, ...)

Look at the number . Every 5th number is a multiple of 5 (5, 55,610, ...)

And so on (every n th number is a multiple of).

1/89 = 0.011235955056179775...

Notice the first few digits (0, 1, 1, 2, 3, 5) are the Fibonacci sequence?

In a way they all are, except multiple digit numbers (13, 21, etc) overlap, like this:

Fibonacci Words
by Rod Pierce
Terms Below Zero

The sequence works below zero also, like this:
(Prove to yourself that each number is found by adding up the two numbers before it!)
In fact the sequence below zero has the same numbers as the sequence above zero, except they follow a +-+- ... pattern. It can be written like this:

Which says that term "−n" is equal to times term "n", and the value neatly makes the correct +1, −1, +1, −1, ... pattern.

History

Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before!

About Fibonacci The Man

His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.

"Fibonacci" was his nickname, which roughly means "Son of Bonacci".

As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble! Thank you Leonardo.

Fibonacci Day

Fibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" which is part of the sequence. So next Nov 23 let everyone know!

1738, 8338, 8339, 8340, 8341, 8343, 3012, 3071, 8841, 8367

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The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it: the 2 is found by adding the two numbers before it (1+1), the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3), and so on!

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Plants have different shaped leaves to cope with different environmental conditions. But many plants change the shape of their leaves over time and space! Why? Have you ever wondered why the shape of leaves are so different among plants? Some can be simple ellipses, some long and thin, some short and broad,...

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Science, Technology, Engineering and Math-the subjects called STEM-continue to be a major focal point in education. This urgent focus on STEM came from the growing concern that education was not providing the building blocks necessary for students to achieve successful future employment in an increasingly technical world.

The goal of focusing on STEM is to provide today's young people with the technical, critical thinking, communication and problem-solving skills they will need tomorrow to compete and succeed in a modern job market.

The theory and research behind STEM education has continued to mature, and today there are a growing group of advocates who believe that STEM is missing a key component. That component is the arts! A growing number of educators would like to add art to STEM to turn it into STEAM.

Is STEAM simply a grab for the spotlight from the liberal arts community? As an education professional with 25 years of teaching experience, I am always wary of new acronyms. In education, trends and initiatives come and go. Most initiatives fade quickly, without a positive effect on the actual transfer of knowledge from the teacher to student. Sometimes it's a lack of funding, sometimes it's a bad idea, but many times a new idea fails because it doesn't take into account the myriad demands already in place on teachers and students.

As a newly trained science teacher in the mid-'90s, I did some eye rolling when STEM was first introduced. I was successfully teaching science; how was calling it STEM going to make any difference? Well, history has shown how young and naive I was, and STEM research and implementation has continued to get stronger. The STEM movement has provided a common focus for distilling the skills society needs for a complex future. STEM initiatives have allowed educators to shift their focus from cramming content to practicing the skills that are needed to be technically literate. Science teachers have transitioned from rote blackboard learning and constrained dry recipe card experiments to more fluid, student-centered activities. Today, the focus on STEM has created activities that revolve around critical thinking, problem-solving, communication and collaboration. Will the addition of art add or detract from the successes STEM education has shown?

Many see art and science as being direct opposites. However, this is not true.
Great scientists-like artists-need to be builders, inventors and dreamers. Take Leonardo da Vinci, a great scientist and an amazing artist: This combination is not as rare as you might think. Scientists who have won the Nobel Prize are 17 times more likely than the average scientist to be a painter, 12 times as likely to be a poet and four times as liked to be a musician. There is something about having an artistic side that helps with having success in STEM fields. Expression through art encourages creativity, play and innovation. These are all traits needed for scientific breakthroughs.

Mae Jemison, the first African American woman in space, once said "The difference between science and the arts is not that they are different sides of the same coin ... or even different parts of the same continuum, but rather, they are manifestations of the same thing. The arts and sciences are avatars of human creativity." Research has shown that there is a strong connection between art and science, as both inspire and demand creative thinking.

Adding art is not about spending less time on STEM, it's about using art to inject a sense of play and spark a student's imagination.
Art encourages creative thinking and innovative interpretations. It is important to note that in this context, the word art is used to represent the full spectrum of the liberal arts: language, social studies, physical art, fine art, music and design. Exploring the use of art can provide young people with new and imaginative opportunities for communication and expression. How can a new design be presented? What is the best way to communicate a finding or discovery? How can a prototype be built? The creative processes behind art can be used to drive innovation and find inventive solutions to problems. The addition of art themes inspires young people to be creative and communicate their ideas and findings.

Art can also serve as a pathway to STEM for traditionally underrepresented students.
Not everyone fits the profile for a traditional scientist, and STEM careers today are varied and wide-ranging. The addition of art can provide another avenue for young people to experience success in STEM and aid them in learning the skills they need to be successful in the 21st century. Additionally, it can provide non-science professionals the inspiration that they need to add STEM to their curriculum. If the addition of art provides another means of motivation for STEM learning, then STEAM does not take anything away from STEM, but only adds to it.

I recommend that STEM goes full STEAM ahead. Not only does STEAM roll off the tongue a little easier, but adding art to STEM helps to inspire creativity and imagination. It can improve communication skills, and has the power to open up the fields of STEM to a more diverse pool of educators and learners. Regardless of our aptitudes, we must all live in this very modern and technical world. The greater the number of young people we can get to identify with STEM learning, the more success they will have later in life.

Celebrated physicist Richard Feynman once said, "Scientific creativity is imagination in a straitjacket." Perhaps the arts can loosen that restraint, to the benefit of all.
Contributed by Andy the Science Wiz, NAA STEM Specialist.

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Science, Technology, Engineering and Math-the subjects called STEM-continue to be a major focal point in education. This urgent focus on STEM came from the growing concern that education was not providing the building blocks necessary for students to achieve successful future employment in an increasingly technical world.

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"Engineers focus on how it works," said Jenni Buckley, an assistant professor of mechanical engineering for the program. "Artists focus on the user experience."

Few schools actually require engineering students to take art, but the University of Illinois comes close. Mr. Leake incorporates freehand sketching and computer-aided design in his engineering graphics class. Many universities have abandoned such a class altogether, or focus on computer drawing.

Mr. Leake, whose first degree is in art history, believes that learning to make even rudimentary drawings is critical to development as an engineer. "Typically, engineering students are not comfortable with sketching," he said. "They say, 'Oh, I can't draw.' " But being able to quickly sketch to communicate an idea, he said, "is an enormously useful tool." It also helps "see" an idea. "To do engineering you've got to be able to visualize."

The Rhode Island School of Design thinks so much of the need to collaborate that it is spearheading a national initiative to incorporate art and design in STEM education - what it calls STEM to STEAM (as in science, technology, engineering, art and math). Art education, they argue, teaches the kind of risk-taking and creative problem-solving that can be applied to, say, health care and climate change.

In one independent project, R.I.S.D. architecture and design students built an 800-square-foot solar house with engineering majors from the school up the hill, Brown. The project, which culminated in a textile-draped, Flintstones-meets-Jetsons creation called Techstyle Haus, was one of two American entries in the 2014 Solar Decathlon Europe in Versailles, France.

Isby Lubin, a Brown engineering major, said R.I.S.D. design students helped her understand how to effectively use the space within the structure. She learned a lot about structural design, she said, and novel uses for strong, lightweight materials. "It's been really amazing to work with R.I.S.D. students because of how focused they are on design," Ms. Lubin said. "We were able to meet in the middle because we're all trained with a really strong foundation. It's just in different things."

John Maeda, who championed STEM to STEAM as president of R.I.S.D. from 2008 to 2013, has degrees in electrical engineering and computer science as well as classical design. In a commentary last year for Scientific American, he wrote this about art/science synergy: "Both are dedicated to asking the big questions placed before us: 'What is true? Why does it matter? How can we move society forward?' Both search deeply, and often wanderingly, for these answers."

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"Engineers focus on how it works," said Jenni Buckley, an assistant professor of mechanical engineering for the program. "Artists focus on the user experience." Few schools actually require engineering students to take art, but the University of Illinois comes close. Mr. Leake incorporates freehand sketching and computer-aided design in his engineering graphics class.

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STEAM represents a paradigm shift from traditional education philosophy, based on standardized test scores, to a modern ideal which focuses on valuing the learning process as much as the results. In essence, we dare our students to be wrong, to try multiple ideas, listen to alternate opinions and create a knowledge base that is applicable to real life as opposed to simply an exam.

Deron Cameron
Former UPES Principal - US's 1st STEAM Certified School
Current TCSS Curriculum Coordinator

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STEAM represents a paradigm shift from traditional education philosophy, based on standardized test scores, to a modern ideal which focuses on valuing the learning process as much as the results. In essence, we dare our students to be wrong, to try multiple ideas, listen to alternate opinions and create a knowledge base that is applicable to real life as opposed to simply an exam.

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STEAM has since gained momentum across the globe-including on Capitol Hill-and is now widely adopted by institutions, corporations and leaders. Even the Sesame Workshop updated its longstanding STEM curriculum to STEAM as a means of reinforcing the ongoing value of the arts and humanities.

Today STEAM can be seen in practice across RISD's curriculum from, for example, the Brown|RISD Dual Degree program to research and experimentation in the Co-Works Research Lab and the Nature Lab to graduate degree programs such as Digital + Media and a partnership with Marine Affairs at the University of Rhode Island to the Computation, Technology and Culture concentration and in studios across disciplines, including a longstanding NASA studio in Industrial Design.

For more information, contact Jaime Marland, senior director of Public Relations.​

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In 2010, RISD began to champion the addition of art and design to STEM education and research, toward creating STEAM, an educational model that inspires creative innovation.

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The Institute for Arts Integration and STEAM

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STEAM is an educational approach to learning that uses Science, Technology, Engineering, the Arts and Mathematics as access points for guiding student inquiry, dialogue, and critical thinking.

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As we highlighted in a previous post Adinkra symbols are a much-referenced communication system that has endured to present day. Adinkra symbols carry within them centuries of wisdom and are among one of the African continent's oldest writing systems. The symbols have inspired designers and artists the world over who have drawn on the distinctive graphic shapes to create anything from jewellery to patterned textiles. We introduce 5 contemporary African brands referencing the symbols in their designs, and in doing so giving them relevance in a modern day and age.

Divine Chocolate - Luxury Packaging

Majority owned by the cacao farmers cooperative, Kuapa Kokoo in Ghana, gourmet chocolate brand Divine Chocolate chose to encase its luxury confectionery with elegant packaging covered in Adinkra symbols, each selected to communicate the social mission driving the brand.

AMWA by Chrissa Amuah - Textile Prints

AMWA creates textiles and interior textiles inspired by the wisdom and meaning found in the different Adinkra symbols and Ghanaian proverbs. The symbols are turned into decorative prints resulting in striking interior products such as cushions and table lamps.

Mary Jean - Jewellery Design

Mary Jean's Adinkra Collection features handmade jewellery that combines West African culture and South African craftsmanship and is inspired by the beauty and simplicity of the bold, geometric patterns and meaning of Adinkra symbols.
YSWARA - Sankofa Teapot
Luxury tea brand YSWARA created a line of tea drinking accessories to complement the tea drinking experience, among their commissions was the majestic Akan tea set featuring a black earthenware teapot rimmed with gold detailing, its form representing the Sankofa, an Adinkra symbol of a bird with its head and neck gracefully curved backwards, and in the Twi language translates to mean 'go back and get it.'

57 Chocolate - Adinkra bars

Artisanal bean to bar chocolate brand handcrafted in Ghana 57 Chocolate's product offering includes bite-sized Adinkra bars that as the names suggest are embossed with the symbols.

Who are some of your favourite brands referencing Adinka symbols in their work, do share in the comments.

- The Editorial Team

[Image credits: The images shown are sourced from/belong to in order of appearance; Fashion Ghana, Divine Chocolate, AMWA Designs; Mary Jean, YSWARA, 57 Chocolate. If downloaded and used elsewhere please credit accordingly.]

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Design Inspired by the Decorative Forms Of Adinkra Symbols

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As we highlighted in a previous post Adinkra symbols are a much-referenced communication system that has endured to present day. Adinkra symbols carry within them centuries of wisdom and are among one of the African continent's oldest writing systems. The symbols have inspired designers and artists the world over who have drawn on the distinctive graphic shapes to create anything from jewellery to patterned textiles.

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3rd Space is the Place to Cultivate & Illuminate.               ...Welcome to Your Zone!

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Physicists Michael Faux and Sylvester James Gates and their collaborators have developed "Adinkras" which they describe as a "graphical technology for supersymmetric representation theory". They...

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Chapter 5: Adinkra Symbols is full of activities related to the use of adinkra symbols in math and science.
https://csdt.rpi.edu/culture/legacy/teaching/papers/Ch%205AdinkraSymbols%20.pdf

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Symbols of Power: Adinkras and the Nature of Reality

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Physicists have long sought to describe the universe in terms of equations. Now, James Gates explains how research on a class of geometric symbols known as adinkras could lead to fresh insights into the theory of supersymmetry - and perhaps even the very nature of reality.

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Adinkra is a printed or stamped traditional cloth made by the Ashanti people in Ghana, especially in the village of Ntonso. Adinkra (ah-DEENK-rah) symbols have been used in Ghana on clothes, walls, pottery and as logos since the early 1800's, when King Adinkra was a king from the Ivory Coast. The symbols each had a special meaning, and some have been passed on for over 100 years. Show your children these symbols, and talk to them about the meaning, the history, and techniques before beginning the art project below.

The adinkra symbols each have a name, and have a great meaning based in universal human values such as family, integrity, tolerance, harmony, determination among many others. Their names come from the language of the Ashante people, Twi. To make the adrinkra cloths, calabash gourds are carved and mounted on sticks. The dye is made by boiling the bark of the Kuntunki Tree with iron slag, to form a paste called adrinkra aduru. By dipping the symbol block into the paste ink, and then stamping it onto the cloth in linear designs, the cloth makers repeat a process that has not changed much in over a century.

Tribal chiefs will often times wear symbols that promote leadership, and thinking ahead. Brightly colored cloth called Kasaida is often worn for festivals. At funerals, mourning cloths are made with exquisite designs of symbols of respect for the departed loved one.

If you are interested in traveling to see textile workers, I recently learned of a tour group called Behind The Scenes Adventures, that specializes in trips to remote villages where the people still make all their own exquisite textiles (including a trip to Ghana to see how adinkra is made!). The pictures shown here were taken on one of these trips, and are used with permission by Cynthia Samaké © from www.btsadventures.com.

Adinkra Symbols

www.adinkra.org This web site has an adinkra symbol index and their explanations, plus downloadable adinkra symbols (right click, and save). The symbols and their explanations that you see on this page are from adinkra.org:
"African symbols known as adinkra are ubiquitous in Ghana, a beautiful West African country on the Atlantic, situated between Cote d'Ivoire and Togo. On cloth and walls, in pottery and logos, these Asante tribe symbols can be found everywhere. This site's mission is to make available high-quality renditions of these African symbols at no cost for personal and non-profit uses."

Adinkra Art Project

I found the following art project, designed to teach children about Ghanian adinkra print-making. The designer of the project, and author of the blog " A Faithful Attempt " is "Miss:" a K-12 Art Teacher who loves teaching Art and seeing the variety of creative solutions students come up with. She has taught Art in international schools around the world including the Caribbean, Southern Africa, France and Canada.

Here is her art project, West African Adinkra Printmaking, in her own words, and with pictures of her students in class. Thank you so much for allowing us to share this fantastic Art opportunity!

This is a West African printmaking project I did a few years ago with some Grade 6 students. For this project, instead of having students carve their stamps (which I have done before with knives and potatoes, but it's tricky with the knives and the potato doesn't seem to last long enough to finish the project), we drew our designs onto flat kitchen sponge cloths (from the Dollar Store). I believe fun foam sheets would also work well.

I gave the students handouts of real symbols and their meanings for inspiration. Students came up with their own design and it had to symbolize something personal to them.

Cut out the design and glue it onto a square of thick cardboard.

Paint the sponge stamp with black tempera or acrylic paint and test it in a sketchbook or a scrap piece of paper. Students needed to figure out for themselves how much paint to apply and how best to apply pressure.

Voilà! A perfect stamp! For our good copies, students simply printed on large white paper. Of course, you could use real fabric.

Ok, so students are stamping away, building up their design. I asked for a symmetrical design but a lot of students went crazy with their own patterns.... Next time I teach this, I will insist the patterns are symmetrical and much closer together. I think, perhaps, some students got bored and just started randomly printing just to fill the paper....it can be a tedious and repetitive process. Next time, I need to teach this to a older grade or use a smaller sheet of paper.

Once the printing was finished and dry, students added 'stitch' marks with oil pastels to create panels. Ta da!

Additional Resources
If you would like to read more (as an adult) here is an excellent resource, with explanations of the symbols, techniques, history, and instructions on making your own stamp: The Adinkra dictionary: A visual primer on the language of Adinkra by W. Bruce Willis.

Here is an explanation from PBS on adinkra cloths and by " The Adinkra Story" by Oxfam. Finally, see what the Ghana Tourism Board has to say about Adinkra.

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Adinkra Fabric Painting of Ghana: Lesson + Art Project

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Adinkra is a printed or stamped traditional cloth made by the Ashanti people in Ghana, especially in the village of Ntonso. Adinkra (ah-DEENK-rah) symbols have been used in Ghana on clothes, walls, pottery and as logos since the early 1800's, when King Adinkra was a king from the Ivory Coast.

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Inscribing Meaning: Adinkra / National Museum of African Art

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Adinkra cloth is stamped and patterned with traditional Ashanti symbols. Each symbol has its own meaning. People in Ghana decorate the cloth by using a black dye made of bark. This dye is called Adinkera aduru, and it is what gives the cloth its name.

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Adinkra Printing of Ntonso-Ashanti, Ghana

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Adinkra printing in Notnso-Ashanti, Ghana, Africa.

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Adinkra is hand-printed fabric made by the Asante people of Ghana. Create your own Adinkra stamps in this activity from Zoom.

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Putting the A in STEAM (science, technology, engineering, art, and math) is often treated as an afterthought. Yet, art has always played a major role in helping us expand and appreciate new science technologies.

Photo credit: mederndepe via flickr (CC BY-SA 2.0)

To develop a complete mind; study the science of art; study the art of science. Learn how to see. Realize that everything connects to everything else. -- Leonardo Da Vinci

Art continues to remain marginal in education, and I believe this is why: Despite tremendous growth in technology, STEM industries, and education, we are stuck in a rut in our politics, our economy, and the fight for health and fairness for most people.

Art makes us more human and empathetic. Without art, it is hard to imagine the lives of other people, other creatures, and the possibilities of other realities in general. Because of this deficit in art education, young people have tremendous faith in the coolness and remarkable evolution of their gadgets, but not much faith in themselves and other humans to grow and evolve.

Putting the A for art in STEM (science, technology, engineering and math) to make STEAM is too often treated as an afterthought. Yet, art has always played a major role in helping us expand and appreciate new science technologies, from the printing press to the smart phone. What would these technologies mean without poetry, movies, music, and smart visual design? Art helps give humans the desire and inspiration to invest great energy and resources into STEM.

Art's relationship to STEM has long been obvious to me. When I first got out of art school one of my first professional jobs was in Silicon Valley. After a stint as an intern at Microsoft and a nine-month contract at Starwave -- a now defunct company started by Microsoft co-founder Paul Allen -- I was employee number five at a startup near Palo Alto.

This was in the 90s, and back then, one could still have pie-in-the-sky notions about what technology would do for society. My dream was to bring imaginative worlds alive using 3D technology and games. While much of this has come true, I am mostly disillusioned by how militaristic and combat-oriented most major gaming franchises have become, and I think this failure is due to art's second-class status in education.

So, while we watch technology's growth, let's make sure we grow along with it. We do this through our poetry, our dance, our music, our visual art, and our literature. We push the potential for our hearts to grow.

A Call to Action

So, let me propose an amendment to Moore's law. Moore's Law, which was proposed by the co-founder of Intel -- Gordon Moore -- in 1965, said that the power of computer technology will double every year. This has held true until now.

My amendment only proposes that we grow along with it in terms of more compassion, in terms of more imagination, in terms of our desire to do more towards endeavors that are more important than our smart phones. Let's call it the More Amendment.

This is where art education counts. Art grows the heart and the imagination so that our science, technology, engineering, and math will reflect what is best in us. Through art education, Silicon Valley will be the afterthought, and our students will be more excited by the future of themselves.

# data[].attributes.attachment_link.title
More Heart, More Art Through STEAM | Edutopia

# data[].attributes.attachment_link.description
Putting the A in STEAM (science, technology, engineering, art, and math) is often treated as an afterthought. Yet, art has always played a major role in helping us expand and appreciate new science technologies. Photo credit: mederndepe via flickr (CC BY-SA 2.0) To develop a complete mind; study the science of art; study the art of science.

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.

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George Lucas Educational Foundation

The benefits of movement in the classroom aren't limited to younger students. Pairing new words and concepts with gestures or dance moves locks in understanding-and active brain breaks prime students to learn even more.

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A free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education.

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https://www.edweb.net/creativity This site is a great online learning community for educators.

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I have a great interest in and passion for Adinkra symbols and wanted to apply this symbology to my STEAM studies. This site is a great place to begin learning more about Adinkra symbols.

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An illustrated guide to the African symbols called Adinkra used in Ghana, West Africa, with an adinkra index and high-quality adinkra images.

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Great for student feedback and collecting data.

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The Adinkra dictionary: A visual primer on the language of Adinkra

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Adinkra is the name given the colorful, hand-painted and hand- embroided cloth used for mourning by the Akan people of Ghana and Cote D Ivore. Stylistic symbols called adinkra symbols are printed on these cloths. The cloth and symbols express the wearer s feeling and sentiment about the deceased....

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https://csdt.rpi.edu/culture/legacy/african/adinkra/geometry.html

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Many of the Adinkra symbols incorporate elements of transformational geometry in their design. The following pages show adinkra symbols using translation, reflection, dilation, and rotation.

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com April 2010
A Mathematical Analysis o Akan Adinkra !ymmetry
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
2
"ontents
#ntrod$ction %
&asic 'ro$p (heory and the )ihedral 'ro$p *
-&rie !ketch o 'ro$p (heory *
-(he )ihedral 'ro$p +
(he )ihedral ,ro$p and Adinkra symbol symmetries -
- (he Method -
- ./planation o 0es$lts 1
Where Mathematics meets Metaphysics 10
"oncl$sion 11
0eerences 12
Appendi/ A2 ./amples o Adinkra !ymbol !ymmetries 1%
Appendi/ &2 ./amples o Adinkra !ymbols 13
Appendi/ "2 Adinkra !ymmetry )etails 1+
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
%
Introduction
(he Akan 4Adinkra4 symbols are picto,rams and ideo,rams which ha5e come
to be well known as c$lt$ral-lin,$istic symbols o the Akan people o 'hana.
(here are h$ndreds o these symbols. (hey represent ideas s$ch as the
nat$re o the $ni5erse6 political belies and or,ani7ation6 social6 economic and
ethical 5al$es6 aesthetics as well as ideas relatin, to amily (see '. 8. K.
Arth$r4s book Cloth as Metaphor). (hese symbols not only represent speciic
ideas and pro5erbs b$t are also related to other orms o Akan art s$ch as
brick layin, (b$ildin, ho$ses) metal crats6 wea5in, and wood car5in,6 all o
which can display 5ersions o these symbols in their work.
As to the ori,in o these symbols6 there has so ar not been a concl$si5e or
deiniti5e answer. !ome ha5e s$,,ested that the symbols deri5e rom #slamic
talismans. 9thers ha5e pointed o$t that this cannot be the case beca$se o
the block-printin, techni:$e $sed by the Akan (which has not chan,ed in
cent$ries) is dierent rom the writin, br$sh and stick method $sed in
#slamic inscriptions ('. 8. K. Arth$r6 20016 p22-23). What is known or s$re
is that the &ron6 the 'yaman and the )enkyira6 three o the old centers o
Akan c$lt$re6 were in5ol5ed with wea5in, beore the Asante rose to power. #t
is also said that the name 4Adinkra4 comes rom a 'yaman kin, who wore the
cloth. 8or more inormation on the ori,in o these symbols6 see '. 8. K.
Arth$r4s book.
While 0attray p$blished 31 o these symbols in his book Religion and Art in
Ashanti6 '. 8. K Arth$r4s book contains ;11 o these symbols6 altho$,h some
are 5ariations o the same. 9$t o these h$ndreds o symbols there are many
with interestin, symmetrical properties that # became interested in st$dyin,.
Also6 $nlike 0attray4s 31 symbols6 some o the ;11 symbols ,i5en by '. 8. K.
Arth$r contain ideas rom modern times.
#n this paper6 # look at the symmetrical properties o some Adinkra symbols.
Altho$,h not all o these symbols ha5e symmetry6 there is a s$bset o them
that do possess symmetries that it a well st$died ,ro$p known as the
4)ihedral ,ro$p4 that describes symmetries o$nd in art as well as in some
,eometric shapes in nat$re. We shall be lookin, at this some more6 in the
ollowin, pa,es.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
*
Basic Group Theory and The Dihedral Group
i) Brief sketch of Group Theory
'ro$p theory is a branch o mathematics that looks at mathematical
str$ct$res with certain speciic properties. Most common ,ro$ps are inite
str$ct$res that ha5e internal consistency. 8or a mathematical str$ct$re to be
classiied as a ,ro$p6 it has to satisy certain conditions. (here is an
operation which when perormed on one member o the ,ro$p ,i5es a res$lt
that points to another member o the ,ro$p. (here are also the concepts o an
4identity46 the presence o an 4in5erse4 or each element and another concept in
mathematics called 4associati5ity4.
(here are many6 many dierent kinds o str$ct$res that can be classiied as
,ro$ps6 b$t as a simple e/ample let $s $se the n$mbers called 4inte,ers46
which most people are amiliar with. (he inte,ers are n$mbers like ... -%6 -26
-16 06 16 26 %6 ... (he dots beore and ater the list o n$mbers says that the list
o n$mbers ,oes on ore5er in each direction6 positi5e and ne,ati5e.
As ar as the inte,ers are concerned6 the 4identity4 is the n$mber 7ero. What
this means is that any n$mber added to 7ero will ret$rn that n$mber. !o 1 <
0 = 1> -3 < 0 = -3> +1 < 0 = +1 etc. All that the identity does is ret$rn the
ori,inal element when the ,ro$p operation is applied. #n the case o inte,ers6
the ,ro$p operation is addition so when yo$ take any other element o the
,ro$p o inte,ers to,ether with the identity (7ero) and yo$ apply the ,ro$p
operation (addition) to these two elements yo$ ,et the non-identity element
(i.e. the other n$mber6 not 7ero). (hat is what the e/amples abo5e showed.
(he in5erse o an element in a ,ro$p is any other element in the ,ro$p which6
when the ,ro$p operation is applied to both elements ,i5es the identity. What
does this mean?
@et $s ret$rn to o$r ,ro$p e/ample6 the inte,ersA @et $s choose any n$mber6
say +. What we want is to choose another n$mber so that when that n$mber
is added to + will ,i5e $s 7ero. Bes6 yo$ ,ot itA What we need is to choose -+6
so that + < (-+) = 0. #n this case6 we say that or o$r ,ro$p (inte,ers) with
,ro$p operation addition6 the in5erse o the n$mber + is -+ and the in5erse o
the n$mber -+ is +6 beca$se when both n$mbers are added to,ether6 we ,et
the 4identity46 which
*
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
we ha5e already said is....7ero.
(he inal re:$irement or a ,ro$p is this idea called 4associati5ity4. All that
this means can be demonstrated with an e/ample2
1 < (2 < %) = (1 < 2) < % = +
!omeone who looks at this e/ample may say that we ha5e not done anythin,.
&$t this is incorrect. We $se &#)MA! (some people learnt this as 4&9)MA!4)
to e5al$ate the abo5e e/press. 4&#)MA!4 stands or 4&rackets6 #nde/6
)i5ision6 M$ltiplication6 Addition6 !$btraction46 while in &9)MA!6 the 494
stands or 4order46 as in6 what somethin, is the power o. !o the two terms are
essentially the same. (hey show which operations to work beore which.
What the e/ample abo5e shows is that the arithmetic operation 4addition4
satisies this condition called 4associati5ity4 when applied to inte,ers. (his
does not always work with e5ery arithmetic operation. @et $s test this with
the same n$mbers2
2 / (% / *) = (2 / %) / * = 2*

!o we can say that the arithmetic operation 4m$ltiplication4 is also
4associati5e4 when applied to inte,ers. What abo$t s$btraction?
2 - ( % C *) = % which is not e:$al to (2 C %) C * = -3
!o we can say that the arithmetic operation 4s$btraction4 is not associati5e
when applied to inte,ers. (he same can be said o the arithmetic operation
4di5ision46 which shall now be shown2
2 D (% D *) ,i5es 2.+++ (rec$rrin,) while (2 D %) D * ,i5es 0.1+++ (rec$rrin,) so
the two e/pressions are dierent dependin, on where the brackets are
placed.
!o associati5ity means Ewithin an e/pression containin, two or more
occ$rrences in a row o the same associati5e operator6 the order in which the
operations are perormed does not matter as lon, as the se:$ence o the
operands is not chan,ed.F (Wikipedia)
(hat ends this brie treatment o basic ,ro$p theory. Gow let $s relate ,ro$p
theory ideas to the )ihedral.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
+
ii) The Dihedral Group
(he dihedral ,ro$p is the ,ro$p o symmetries o a re,$lar poly,on that
incl$de relections and rotations. (he dihedral ,ro$p is a type o 4symmetry
,ro$p4.
# yo$ consider an e:$ilateral trian,le (trian,le with all three sides o e:$al
len,th6 and all three an,les o e:$al si7e)6 and i yo$ were to label the three
corners A6 &6 and "6 yo$ can ima,ine rotatin, the trian,le clockwise so that A
takes the position o &6 & takes the position o " and " takes the position o
A. (his can be seen as one rotation. (he an,le o rotation will be +0 de,rees6
since each an,le in an e:$ilateral trian,le has that an,le.
-------H
8i, 1 C 0otatin, a trian,le +0
o
clockwise
@ikewise6 one can see how the trian,le can be rotated a,ain and a,ain so that
the corner labelled A will ret$rn to its ori,inal position. # one were to co$nt
the n$mber o rotations needed to do this6 the answer will be % (yo$ can try it
i yo$ like).
8i, 2 C @ines o symmetry o a trian,le
9ne can also draw lines o symmetry as shown in the i,$re abo5e. (he
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
;
trian,le has three o them6 while the s:$are has o$r o them. # we were to
carry o$t the symmetry operations on a s:$are whose * corners are labelled
(A6 &6 " and )) and which has * lines o symmetry6 we will prod$ce the table
o operations below2
↓→ 0
0
0
10
0
1-0
0
2;0
I J ) )4
0
0
0
0
0
10
0
1-0
0
2;0
I J ) )4
0
10
0
10
0
1-0
0
2;0
0
0
) )4 J I
0
1-0
0
1-0
0
2;0
0
0
0
10
J I )4 )
0
2;0
0
2;0
0
0
0
10
0
1-0
)4 ) I )
I I )4 J ) 0
0
0
1-0
0
2;0
0
10
J J ) I )4 0
1-0
0
0
0
10
0
2;0
) ) I )4 J 0
10
0
2;0
0
0
0
1-0
)4 )4 J ) I 0
2;0
0
10
0
1-0
0
0
(!o$rce2 "ontemporary Abstract Al,ebra6 p. 23)

8i, % C )-6 the symmetry ,ro$p o a s:$are
&asically this table says that 0
0
is the ori,inal position o the s:$are6 so we
ha5e done nothin, to it. 0
10
is a s:$are that has been rotated 10 de,rees
clockwise. I is the hori7ontal line o symmetry o the s:$are6 J is the
5ertical6 ) is one dia,onal and )4 is the other dia,onal.
(he reason why these operations orm a ,ro$p is that i we take the s:$are
$nder one o the operations and apply another operation to it the res$lt will
be a coni,$ration ittin, one o the ei,ht operations. !o all the operations are
inite6 closed and contained.
(h$s the )ihedral ,ro$p or the symmetries o a trian,le is called )
+
6 beca$se
there are % rotations and % lines o symmetry. (hat ,i5es + possible
operations. (he dihedral ,ro$p or the symmetries o a s:$are is called )
-
6 so
yo$ may ha5e ,$essed where this is all leadin, to. We can state (witho$t
proo) that the dihedral ,ro$p o a re,$lar poly,on with n sides is called )
2n
.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
-
The Dihedral group and Adinkra symbol symmetries
i) The Method
(here are many cases in nat$re where the symmetrical str$ct$re o an obKect
are identical to a dihedral ,ro$p (o order n) or to a s$b,ro$p o a dihedral
,ro$p. (his is the case with crystalline obKects as well as with certain 5ir$ses
and protein str$ct$res. (he e/ample ,i5en in Appendi/ A is a o a snowlake
that has the same symmetries as the dihedral ,ro$p )
12
(i.e. the symmetries
o a re,$lar he/a,on).
#t is :$ite well known that symmetrical art oten shows properties that can
be described by a dihedral ,ro$p. (his is the main reason why # chose to
e/amine the Adinkra symbols to ind o$t i there are partic$lar symmetries
that are more common than others.
#n order to do this6 # e/amined the inde/ o '. 8. K Arth$r4s book Cloth as
Metaphor (p 12- C 1-;) where he lists ;11 Adinkra symbols6 to,ether with
their meanin,s6 pro5erbs and other associations. (his list is perhaps the most
comprehensi5e list o Adinkra symbols in print (to date). #n decidin, which
Adinkra symbols to choose or analysis6 # (s$bKecti5ely) chose those that
looked $ni:$e since some o the symbols in the inde/ are 5ariations o the
same. 9$t o the ;11 symbols # sampled -* o them6 which prod$ced a sample
o appro/imately 11.+-L o all the symbols listed. (he res$lt o the analysis is
shown in the table below6 while the more e/tensi5e list can be o$nd in
Appendi/ ".
Refl/Rot 0 ! " #"
0 2 - 1
$ 1*
%1 1
! 3
" 1
#" 3
8i, * C Adinkra symmetries. !$mmary o sample o -* symbols
@ookin, at Appendi/ A will ,i5e some idea o how some Adinkra symbols can
be analysed to obtain their symmetries.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
1
i) %&planation of Results
(he table in i,$re * (abo5e) shows the relection and rotational symmetries
o each symbol analysed (see Appendi/ A or how the symbols were analysed).
What i,$re * shows is that there are many dierent kinds o Adinkra symbol
symmetries. !ome shapes ha5e no relection or rotational symmetries while
others ha5e (potentially) ininite relection and (potentially) ininite
rotational symmetries (see n$mbers 3 and 2* in Appendi/ " or e/amples o
these).
8rom the sample o analysed symbols6 3 Adinkra symbols ha5e symmetries
that are identical to the dihedral ,ro$p )
+
(symmetries o a trian,le) and 1
symbols ha5e symmetries identical to the dihedral ,ro$p )
-
. 3 symbols had
symmetries that had more than * lines o symmetry and more than *
rotational symmetries (see n$mbers -6 20 and +0 in Appendi/ "). (hese had
symmetries identical to dihedral ,ro$ps )
1+
and )
%2
.
(here were also shapes that had only one line o relection (i.e either
hori7ontal or 5ertical) or those that had 2 rotational symmetries. Appendi/ "
has more e/amples o these.
&$t by ar the most common were symbols that had 2 lines o symmetry
(hori7ontal and 5ertical) and two rotational symmetries. !hapes o this
nat$re can be seen as Eone i,$re made $p o two identical partsF. (he
identical parts are mirror ima,es o each other. # think this is 5ery
interestin, i yo$ think in terms o an ima,e and its shadow or its mirror.
All the Adinkra symbols that it this 4most common pattern4 all $nder
dihedral ,ro$p )*. (hey are a s$b,ro$p o )
*
witho$t all the transormations
(i.e. no dia,onal relections and two less rotations).
8inally it sho$ld perhaps be mentioned that that dihedral ,ro$p )
n
is a
s$b,ro$p o dihedral ,ro$p )
2n
6 so that )
*
is a s$b,ro$p o )
-
and )
-
is a
s$b,ro$p o )
1+
6 so that )
*
is also a s$b,ro$p o )
1+
. !ince the irst re,$lar 2-
) shape we can ha5e is a a trian,le6 dihedral ,ro$ps start at )
+
and contin$e
on to )
-
6 )
10
etc6 or re,$lar poly,ons o si7e %6 *6 36...
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
10
'here Mathematics meets Metaphysics
M$ch as the mathematical symmetries o the Adinkra symbols are
interestin, K$st by themsel5es6 # belie5e that at least some o the Adinkra
symbols encode 5ibrational ener,y patterns. (his belie stems rom what #
ha5e obser5ed in some Gati5e #ndian sand paintin,s6 as well as Iind$ #ndian
yantras and (ibetan mandalas. !ome o the Adinkra symbols are act$ally
(simpliied) carbon copies o patterns o$nd in some sand paintin,s6 mandalas
and yantras.
# belie5e that it may be possible to work o$t the relationship between the
e/ternal symmetries o some Adinkra symbols and their ener,etic-5ibrational
:$alities. Adinkra symbols may be associated with partic$lar colo$rs6
n$mbers and so$nd patterns and hence may be $sed in a kabbalistic way.
#n order to in5esti,ate the 5ibrational ener,ies $nderlyin, some Adinkra
symbol symmetries6 # $sed an amethyst pend$l$m to dowse selected
Adinkra symbols. # obser5ed that o$r mo5ements maniested2 west-east6
north-so$th6 circ$lar (clockwise) and circ$lar (co$nter clockwise). 8$rther
work is bein, done in this re,ard to determine whether it is possible to come
$p with a schema showin, Adinkra symbols with 5ario$s adKoinin, :$alities.
(he symmetrical properties o these symbols may pro5ide a helpin, hand in
i,$rin, o$t this schema.
(he a$thor o this article hopes that other spirit$ally oriented in5esti,ators
interested in Adinkra may cond$ct e/periments and in5esti,ations o their
own and share their res$lts. 9 partic$lar interest is what other indi5id$als
e/perience (so$nd6 colo$r6 mo5ement) when they meditate on or 5is$ali7e
partic$lar Adinkra symbols.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
11
(onclusion
Altho$,h it has emer,ed rom this in5esti,ation that the most common
symmetry or (symmetrical) Adinkra symbols is two lines o relection and
two rotations (to brin, the shape back to its ori,inal position)6 the story abo$t
the mathematical and possible metaphysical properties o Adinkra symbols is
not o5er. #n act it is only be,innin,A #t is my hope that more in5esti,ations
will occ$r s$rro$ndin, these symbols in order to learn more abo$t them.
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
12
R%)%R%*(%+
'. 8. K. Arth$r6 Cloth as Metaphor: (Re)-reading the Adinkra Cloth Symbols
of the Akan of Ghana6 A-oaks Mrintin, Mress2 1111
N. A. 'allian6 Contemporary Abstract Algebra6 ). ". Ieath and "ompany2
1110
0. !. 0attray6 Religion and Art in Ashanti6 "larendon Mress6 9/ord2112;
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
1%
Appendi& A , %&amples of Adinkra +ymbol +ymmetries
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
13
Appendi& B , %&amples of Adinkra +ymbols
(!o$rce2 #nternet)
An Adinkra !ymbol6 a snowlake and a Ga5aKo !and paintin,
(!o$rce2 #nternet)
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
1+
Appendi& ( , Adinkra +ymmetry details
O 0eer to Adinkra #nde/ o book Cloth as Metaphor to see which
Adinkra symbols were $sed. (he n$mbers in parentheses
correspond to the symbol n$mber in the inde/ o symbols.
*umber Adinkra *ame Rotational
+ymmetry
Reflection
+ymmetry
1 Abode !antann (1) 0 1
2 'ye Gyame (2) 2 0
% 9domankoma (1%) % %
* !oro ne Asase (1*) 2 0
3 M$r$ (circle) (13) ininite ininite
+ Iann ne s$m (1-) * *
; Asase ye d$r$ (236 2+) 2 2
- Ananse Gtotan (%*) - -
1 !$ns$m (%3) * *
10 Gs$ (*0) 0 1
11 Iye Anhye (*2) 2 2
12 Gyame )$a (3%) * *
1% Kerapa (+1) * 2
1* Momma ye mmbo mpae (;0) 2 2
13 Gkrabea (;3) 2 0
1+ 9w$o Atwede (10) 2 2
1; 9w$o Mpe !ika (1-) 2 2
1- Mema wo hyeden (103) 2 2
11 Woye hwan? (111) 2 2
20 Gsoromma (11+) - -
21 &iribi wo soro (12+) 2 2
22 9hene Adwa (131) 0 1
2% !$mpie (1;*) % %
2* Adinkra hene (1;--1-3) Motentially
ininite
Motentially
ininte
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
23 Aban pa (11%) 2 2
2+ Gk$r$ma kese (113) * *
2; )wennimen (212) 2 2
2- .sono Anantam (222) * *
21 Gkotimseo M$a (2%*) * 0
%0 'yaw$ Atiko (2*;) 2 0
%1 Akoben (23%) 0 1
%2 .kyem (2+1) 0 1
%% 9bi nka obi (2;%) 2 0
%* )wan (ire (2-1) 0 1
%3 Mmara Krado (210) 2 2
%+ .pa (21+) 2 2
%; !epo (211) 0 1
%- Gkonsonkonson (%0*) 2 2
%1 .se ne tekrema (%22) 2 2
*0 Mempasie (%2%) 2 2
*1 &oa me (%%1) 2 2
*2 &oa w4aban (%%+) 2 2
*% 8awohodie (%%1) 2 2
** )$a koro (%*%) 0 1
*3 Adwo (%*1) 2 2
*+ Mpaboa (%3%) 2 2
*; Asase Aban (%3*) % %
*- Asomdwoe 2 2
*1 Asambo (%;3) 2 2
30 Mmora &anyini (*21) 2 2
31 Akoko nan (*2*) 0 1
32 Ab$s$a do $n$ (*3+) 2 2
3% Be papa (*+%) 2 2
3* &$ wo ho (*+*) 2 2
33 Gni aw$ (*;-) 0 0
Written by -K- (akwadapa@hotmail.com) www.theakan.com April 2010
3+ Kata wo de so (*-3) 2 2
3; .nni nsek$ro (*1%) 0 1
3- Wawa aba (30+) 2 2
31 Aya (311) 0 1
+0 W4ano pe asem (32*) 1+ 1+
+1 Aka m4eni (3%0) 0 1
+2 Mekyia wo (3%1) 2 0
+% !aa? (3%+) 2 2
+* Gantie yie (3*2) 2 2
+3 9bra ye bona (3*;) % %
++ Adasa pe mmoboro (3*-) 0 1
+; Iwe yie (33*) 2 2
+- &o wo ho ban (333) 2 2
+1 Iwe w4akan m$ yie (33+) 2 0
;0 Mens$ro wo (331) 0 0
;1 )wen wo ho (3+%) 2 2
;2 &ese saka (3;+) * *
;% Asetena pa (+0*) 2 2
;* !ankoa (+*2) 0 1
;3 Mate Masie (+32) * *
;+ K$ntankantan (+++) * *
;; Gkore (+;0) 2 2
;- 'yina Mintinn (+;2) 2 2
;1 )wen hwe kan (+;%) 2 2
-0 W$d$ nkwanta a (+-%) 2 2
-1 Ab$r$b$ro kos$a (;10) 2 0
-2 Ananse anton kasa (;13) 2 2
-% Ahinansa (;1;) % %
-* Gkabom (;11) 2 0

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com April 2010 A Mathematical Analysis o Akan Adinkra !ymmetryWritten by -K- (akwadapa@hotmail.com) www.theakan.com April 20102"ontents#ntrod$ction %&asic 'ro$p (heory and the )ihedral 'ro$p * -&rie !ketch o 'ro$p (heory * -(he )ihedral 'ro$p +(he )ihedral ,ro$p and Adinkra symbol symmetries -- (he Method -- ./planation o 0es$lts 1Where Mathematics meets

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