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Students will understand what the number π (pi) is and how it is used in mathematics, especially in calculating the circumference and area of a circle.

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The teacher introduces the connection between the number PI and the formulas in which it is used. Then she cites some historical facts about the number PI and some interesting facts.

The number pi appears in several formulas.

It appears in every formula that calculates something for a body that has a curved part or surface.

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(Presentation is made by Gamma)

The Whimsical World of PI.

This presentation shows some facts related to number pi.

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Students will recognize the historical importance of the number π and learn who throughout history has tried to calculate the number π and how.

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Pi () has been known for almost 4000 years-but even if we calculated the number of seconds in those 4000 years and calculated to that number of places, we would still only be approximating its actual value. Here's a brief history of finding π.

The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900-1680 BC) indicates a value of 3.125 for π, which is a closer approximation.

The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π.

The first calculation of π was done by Archimedes of Syracuse (287-212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of π but only an approximation within those limits. In this way, Archimedes showed that π is between 3 1/7 and 3 10/71.

A similar approach was used by Zu Chongzhi (429-501), a brilliant Chinese mathematician and astronomer. Zu Chongzhi would not have been familiar with Archimedes' method-but because his book has been lost, little is known of his work. He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. To compute this accuracy for π, he must have started with an inscribed regular 24,576-gon and performed lengthy calculations involving hundreds of square roots carried out to 9 decimal places.

Mathematicians began using the Greek letter π in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Leonhard Euler, who adopted it in 1737.

An eighteenth-century French mathematician named Georges Buffon devised a way to calculate π based on probability. You can try it yourself at the Exploratorium's Pi Toss exhibit.

Download this article as a PDF.

Shown: Thomas Degeorge (1786-1854), The Death of Archimedes (detail), 1815. Collection of the Musée d'Art Roger-Quilliot Museum [MARQ], City of Clermont-Ferrand, France.

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A Brief History of Pi (π) | Exploratorium

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A Brief History of Pi (π) Pi (π) has been known for almost 4000 years-but even if we calculated the number of seconds in those 4000 years and calculated π to that number of places, we would still only be approximating its actual value. Here's a brief history of finding π.

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Explore what Wikipedia has to say about mathematicians in history who worked to calculate the number π (eg Archimedes, Ludolph van Ceulen)!

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This article is about the mathematical constant. For the Greek letter, see Pi (letter). For other uses, see Pi (disambiguation).

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Guess as many decimal places of PI as possible

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Pi Quiz, Memorize Pi [Easy And Fun Memory Game] | Pi Day

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Recite up to 150 digits of pi using your memory, how many digits can you memorize?

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This video is 18 minutes long and explains in detail how to calculate the number pi and something else... This is just one option, it can be used by the student for self-learning.

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A story about a math class held for Croatian and Spanish students. The topic of the class is the number pi: how it is calculated, applications, and interesting facts...

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Not your computer? Use Guest mode to sign in privately. Learn more about using Guest mode

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This short video demonstrates the connection between physics and mathematics.
Light reflects depending on the angle of incidence – the greater the angle, the more times light reflects inside a circular body, like in a diamond.
This is an example of total internal reflection.
The video also shows how the circumference of a circle was historically approximated – by drawing regular polygons inside the circle.
The more sides the polygon has, the closer its perimeter is to the circle’s circumference.
The diameter remains the same.
Archimedes used a similar method to approximate π – using polygons both inside and outside the circle to find upper and lower bounds.

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How to find Pi in the old times #maths #shorts

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memory PI

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Game

New

The game is now playable on mobile!

Rules

There are an infinite number of digits of pi.
Type as many digits of π as possible to increase your score.
You have 3 seconds to type each digit.
Have fun!

Tips

Press Enter to restart the game.
Enjoy the practice mode to learn the digits of π (the best score is not updated in this mode).

Credits

Memory Pi was created by André Harnist.

Motivation

I wanted to create a simple math game that could entertain anyone to discover some math curiosities.
The symbol π represents a fascinating number and yet its definition is very simple: as the ratio of a circle's circumference to its diameter.
You can train your memory by learning its unpredictable digits!

Contact

A suggestion for improvement, a bug to report?
Do not hesitate to contact me: andre.harnist@inria.fr
Thanks to all the players who expressed interest in this game, and for coming up with some great ideas to improve it!

Websites about π

Thank you for playing!

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The game is now playable on mobile! There are an infinite number of digits of pi. Type as many digits of π as possible to increase your score. You have 3 seconds to type each digit. Have fun! Press Enter to restart the game.

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If you know how... try for yourselves!

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Students will watch a short video with two questions and one task.

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Edpuzzle video lesson. Make any video your lesson. Take a video and crop it, add your voice or embed questions at any point.

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At this link, students can type in their date of birth and they will be given where that sequence of digits falls among the decimals of pi.

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For those that dont remember, PI is the big(*)
number that begins with three.

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(Document is made in Canva)

For homework, students will determine the frequency of individual digits (decimals).
They need to count how often each digit appears among the first 1,000 decimal places.
Statistics show that each digit appears approximately the same number of times.
For example, among the first 100 decimal places, each digit from 0 to 9 appears about 10 times.
The same pattern continues for the first 1,000, 1,000,000 decimal places... the frequency of each digit is always approximately equal.

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Activity 1: Measure and Calculate π!
Activity Description:
In this activity, students find various circular objects (plates, bottle caps, glasses, etc.) and carefully measure their circumference and diameter.
They then calculate the ratio of the circumference to the diameter (C ÷ D) for each object and compare the results.
The goal is to discover that the ratio is always approximately the same and close to the number π (3.14).

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Activity 2: Is the Ratio the Same Regardless of the Circle’s Diameter?
Activity Description:
In this activity, students draw a large circle on a poster or a big sheet of paper.
Using a piece of string, they measure the circumference by wrapping it around the edge of the circle, and they measure the diameter with a ruler.
Then, they investigate how many times the diameter "fits" into the circumference.
Finally, they write down their result and draw what they discovered.
The goal is to approximate the value of π – around 3.14.

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Discover the captivating journey of Pi, the mathematical constant that has intrigued scholars for centuries. In just 60 seconds, explore Pi’s origins from ancient civilizations to its pivotal role in modern mathematics, science, and technology. This video uses compelling stock footage and expert narration to reveal how Pi influences everything from geometry to engineering and cosmology. Perfect for math enthusiasts and curious minds alike, learn why Pi remains a symbol of infinite mystery and scientific breakthrough. Like and share this quick dive into the history and impact of Pi to inspire others with the beauty of mathematics!

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Turn ideas into videos | AI video creator | invideo AI

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Make videos easily by giving a prompt to invideo AI. Ideal for content creators, YouTubers and marketers, invideo AI offers a seamless way to turn your ideas into publish-ready videos with AI.

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The students are doing homework assignments. They are calculating the circumference or the area of a circle.