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Wolfram|Alpha: Making the world’s knowledge computable

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Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

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Minimal Surface -- from Wolfram MathWorld

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Finding a minimal surface of a boundary with specified constraints is a problem in the calculus of variations and is sometimes known as Plateau's problem. Minimal surfaces may also be characterized as surfaces of minimal surface area for given boundary conditions.

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Cauchy problems for the general conformal vacuum field equations in general realativity

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Cauchy problems for the general conformal vacuum field equations in general realativity

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Cauchy problems for Einstein's conformal vacuum field equations are reduced to Cauchy problems for first order quasilinear symmetric hyperbolic systems. The “hyperboloidal initial value” problem, where Cauchy data are given on a spacelike hypersurface which intersects past null infinity at a spacelike two-surface, is discussed and translated into the conformally related picture. It is shown that for conformal hyperboloidal initial data of classH S,s≧4, there is a unique (up to questions of extensibility) development which is a solution of the conformal vacuum field equations of classH S. It provides a solution of Einstein's vacuum field equations which has a smooth structure at past null infinity.

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Did writing your own questions and reading them today lead you to deeper thinking?

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Did writing your own questions and reading them today lead you to deeper thinking?

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Yes, I feel like answering them was harder because i really strived for accurate information in my padlet...

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Answers for questions of article: 10 tricks for....

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Answers for questions of article: 10 tricks for....

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Developing this sort of skill will help reach higher levels of math easier

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Questions for Article: 10 tricks for solving math quickly in your head

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Questions for Article: 10 tricks for solving math quickly in your head

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will
i jump in math skills by developing this sort of skill?
Is this way suggested?
What frame of mind will i develop?
how long does it take to easily get into a habit of it?
Is this more based off memorizing ore developing a good habit?
Is it better to use this way instead of a caluculator?
Can i increase my intelligence by using this daily?

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how to quickly solve math equations in your head

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how to quickly solve math equations in your head

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You don't have to be a math teacher to know that a lot of students-and likely a lot of parents (it's been awhile!)-are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math, improve math skills and understanding, and excel in advanced courses.

If it's your job to teach those, here's a great refresher.

10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

644 + 238

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 - 644 = 6 and 240 - 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 - 8 = 882

So the answer to 644 +238 is 882.

2. Subtracting from 1,000

Here's a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 - 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.

Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

5 x 4 = 20

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.

Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

5 x 3 = 15

4. Division tricks

Here's a quick way to know when a number can be evenly divided by these certain numbers:

10 if the number ends in 0

9 when the digits are added together and the total is evenly divisible by 9

8 if the last three digits are evenly divisible by 8 or are 000

6 if it is an even number and when the digits are added together the answer is evenly divisible by 3

5 if it ends in a 0 or 5

4 if it ends in 00 or a two digit number that is evenly divisible by 4

3 when the digits are added together and the result is evenly divisible by the number 3

2 if it ends in 0, 2, 4, 6, or 8

5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let's use the example of 9 x 3.

Step 1: Subtract 1 from the number that is being multiplied by 9.

3 - 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2: Subtract that number from the number 9.

9 - 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

11 x 25

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

2_5

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

2_7_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

8_(8 +8)_8

(8 + 1)_6_8

9_6_8

There is the answer to 11 x 88: 968

7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

Step 1: Move the decimal point over by one place, 235 becomes 23.5.

Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

8. Quickly square a two-digit number that ends in 5

Let's use the number 35 as an example.

Step 1: Multiply the first digit by itself plus 1.

Step 2: Put a 25 at the end.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

20 x 120

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

10. Multiplying numbers that end in zero

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

200 x 400

Step 1: Multiply the 2 times the 4

2 x 4 = 8

Step 2: Put all four of the zeros after the 8

80,000

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics-and unafraid to work with numbers in the future.

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Tags: Math and Science, Mathematics

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10 Tricks for Doing Math Quickly in Your Head

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You don't have to be a math teacher to know that a lot of students-and likely a lot of parents (it's been awhile!)-are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math, improve math skills and understanding, and excel in advanced courses.

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Differential equations are equations that relate a function with one or more of its derivatives. This means their solution is a function! Learn more in this video.

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General relativity                                                                                          The standard model: Calculus                                                   Pythagorean theorem                                            1=0.999999999999999…                                                                      Special relativity                                                                                      Euler’s equation                                                                                         Euler-lagrange equations and noether’s theorem                                  The callan-symanzik equation                                                                   The minimal surface area equation                                                         The euler line

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General relativity                                                                                          The standard model: Calculus                                                   Pythagorean theorem                                            1=0.999999999999999…                                                                      Special relativity                                                                                      Euler’s equation                                                                                         Euler-lagrange equations and noether’s theorem                                  The callan-symanzik equation                                                                   The minimal surface area equation                                                         The euler line

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A surface M ⊂ R ³ is minimal if and only if it can be locally expressed as the graph of a solution of

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The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day

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The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day

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oh look it's variables! variables are used in most advanced equations such as  the minimal surface area equation. 

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oh look it's variables! variables are used in most advanced equations such as  the minimal surface area equation. 

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While the first two equations describe particular aspects of our universe, another favorite equation can be applied to all manner of situations. The fundamental theorem of calculus forms the backbone of the mathematical method known as calculus, and links its two main ideas, the concept of the integral and the concept of the derivative.

"In simple words, [it] says that the net change of a smooth and continuous quantity, such as a distance travelled, over a given time interval (i.e. the difference in the values of the quantity at the end points of the time interval) is equal to the integral of the rate of change of that quantity, i.e. the integral of the velocity," said Melkana Brakalova-Trevithick, chair of the math department at Fordham University, who chose this equation as her favorite. "The fundamental theorem of calculus (FTC) allows us to determine the net change over an interval based on the rate of change over the entire interval."

The seeds of calculus began in ancient times, but much of it was put together in the 17th century by Isaac Newton, who used calculus to describe the motions of the planets around the sun.

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The 11 Most Beautiful Mathematical Equations

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While the first two equations describe particular aspects of our universe, another favorite equation can be applied to all manner of situations. The fundamental theorem of calculus forms the backbone of the mathematical method known as calculus, and links its two main ideas, the concept of the integral and the concept of the derivative.