## Monday, July 25, 2016

## Friday, July 22, 2016

## Thursday, July 21, 2016

### 10 Math/Number Facts (Vol. #4)

1. Harvard Professor Oliver Knill who has indexed clips from approximately 150 movies featuring mathematics. You can have a look at the list here

2. When website owner of 3.141592653589793238462643383279502884197169399375105820974944592.com has to move page containing 'Pi to one MILLION decimal places' to random index page because servers were getting down by frequent visits by math nerds.

3. 0.999… is the same as 1. Not just very close, but precisely identical:

a = 0.999…

10a = 9.999…

10a – a = 9.999… – 0.999…

9a = 9

a = 1

4. Triangle Dissection Paradox or Missing square puzzle : If you rearrange blocks of first triangle and make second triangle out of it, you will get remaining 1x1 block in second figure.

To find out how it happened, look at the Wikipedia page

2. When website owner of 3.141592653589793238462643383279502884197169399375105820974944592.com has to move page containing 'Pi to one MILLION decimal places' to random index page because servers were getting down by frequent visits by math nerds.

3. 0.999… is the same as 1. Not just very close, but precisely identical:

a = 0.999…

10a = 9.999…

10a – a = 9.999… – 0.999…

9a = 9

a = 1

4. Triangle Dissection Paradox or Missing square puzzle : If you rearrange blocks of first triangle and make second triangle out of it, you will get remaining 1x1 block in second figure.

To find out how it happened, look at the Wikipedia page

5. 1,741,725=17+77+47+17+77+27+57

6. Novemnonagintillion : Ever wonder what a number with 300 zeros after one is called? No? Well who asked you anyway? Actually, it's called a novemnonagintillion . To have a look at the list of names of big number visit BigNumbers

7. Amazing properties of number 9:

12345679 x 9 = 111,111,111

111,111,111 x 111,111,111 = 12345678987654321

1/9 = 0.11111....

8. Rotating number 142857:

142857 x 2 = 285714

142857 x 3 = 428571

142857 x 4 = 571428

142857 x 5 = 714285

142857 x 6 = 857142

And 1/7 = 0.142857...

9. 5141 is the only four digit number that is reversed in hexadecimal.

5141 = 0x1415

10. 88 + 88 + 58 + 98 + 38 + 48 + 78 + 78 = 88593477

Labels:
10 facts,
142857,
9,
big numbers,
geometry,
hexadecimal,
math movie,
Oliver Knill,
paradox,
Pi

### Math Tip : How to check if number is divisible by 7

Cut the number into 2 parts: the last digit and everything else before that. You now have 2 numbers. Take the number that was the last digit and multiply it by 2. Now subtract that from the other number. If this new number is also divisible by 7, then the original number was divisible by 7.

Is 854 divisible by 7?

Number A: 85

Number B: 4

Number A - 2 * Number B = 85 - 2 * 4 = 77

77 is most certainly divisible by 7, therefore 854 is also divisible by 7

Is 854 divisible by 7?

Number A: 85

Number B: 4

Number A - 2 * Number B = 85 - 2 * 4 = 77

77 is most certainly divisible by 7, therefore 854 is also divisible by 7

## Wednesday, July 20, 2016

### Math trick using number 73

Find a piece of paper, a pencil, a calculator and a friend

Write 73 on a piece of paper, fold it up, and hand it to your unsuspecting friend.

Ask your friend select a four-digit number and enter it twice into a calculator.

Ask your friend to divide this number by 137.

Now ask your friend to divide the answer by his original four-digit number

Ask your friend to look at the folded piece of paper.

You are a Math Magician!

Entering a four-digit number twice (23452345) is equivalent to multiplying it by 10001.(2345 x 10001 = 23452345).

Since 10001 = 73 x 137, the eight-digit number will be divisible by 73, 137, and the original four-digit number.

Source

Write 73 on a piece of paper, fold it up, and hand it to your unsuspecting friend.

Ask your friend select a four-digit number and enter it twice into a calculator.

*Example*: 23452345Ask your friend to divide this number by 137.

*Example*: 23452345 / 137 = 171185Now ask your friend to divide the answer by his original four-digit number

*Example*: 171185 / 2345 = 73Ask your friend to look at the folded piece of paper.

You are a Math Magician!

**Why this happens**:Entering a four-digit number twice (23452345) is equivalent to multiplying it by 10001.(2345 x 10001 = 23452345).

Since 10001 = 73 x 137, the eight-digit number will be divisible by 73, 137, and the original four-digit number.

Source

## Sunday, July 17, 2016

### 10 facts about Tesseract cube

1. The tesseract is a four dimensional cube. the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.

2. The word tesseract was coined and first used in 1888 by British mathematician Charles Howard Hinton in his book A New Era of Thought. Hinton was also famous for his set of colored cubes that he claimed could be used to help people visualize the fourth dimension.

3. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid,[1] cubic prism, and tetracube (although this last term can also mean a polycube made of four cubes). It is the four-dimensional hypercube, or 4-cube as a part of the dimensional family of hypercubes or "measure polytopes".

4. The number of vertices doubles with every dimension: the segment has 2 of them, the square 4, the cube 8, and the tesseract has 16.

5. In addition to 16 vertices, the tesseract has 32 edges, 24 squares, and 8 cubes - all in 1 tesseract.

6. In Madeleine L'Engle's novel A Wrinkle in Time, the characters in the story travel through time and space using tesseracts. The book actually uses the idea of a tesseract to represent a fifth dimension rather than a four-dimensional object (and also uses the word "tesser" to refer to movement from one three dimensional space/world to another).

7. In the science fiction novel Factoring Humanity by Robert J. Sawyer, a tesseract is used by humans on Earth to enter the fourth dimension and contact another civilization on a planet orbiting the star Alpha Centauri A. The hypercube initially exists as a series of connected 3-dimensional cubes, which represent a hypercube that has been unfolded. Refolding the cube in a certain specific manner causes the reformation of the hypercube in 4 dimensions.

8. In John Mighton's play, Half Life, one of the characters (an aging mathematician) builds a tesseract (or rather, the projection of a tesseract) out of popsicle sticks. In the Season 1 episode "Rampage" of the television crime drama NUMB3RS, main character mathematician Charlie Eppes discovers a popsicle-stick tesseract (projection) he built as a boy.

9. If you are bored with 3D Rubik's cube, you can try your hands on Rubik's tesseract like shown in this video

10. Mathematically, "time" is not "the fourth dimension"; "space time" is a particular physical model, but in mathematics, 4-dimensional Euclidean space is simply the set of all ordered 4-tuples (a,b,c,d)(a,b,c,d) with a,b,c,da,b,c,d real numbers, satisfying certain axioms. Time doesn't enter into it. Arturo Magidin's comment at math.stackexchange.com

1. Wikipedia

2. Cut The Knot!

3. Wolfram Mathworld

4. The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover

2. The word tesseract was coined and first used in 1888 by British mathematician Charles Howard Hinton in his book A New Era of Thought. Hinton was also famous for his set of colored cubes that he claimed could be used to help people visualize the fourth dimension.

3. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid,[1] cubic prism, and tetracube (although this last term can also mean a polycube made of four cubes). It is the four-dimensional hypercube, or 4-cube as a part of the dimensional family of hypercubes or "measure polytopes".

4. The number of vertices doubles with every dimension: the segment has 2 of them, the square 4, the cube 8, and the tesseract has 16.

5. In addition to 16 vertices, the tesseract has 32 edges, 24 squares, and 8 cubes - all in 1 tesseract.

6. In Madeleine L'Engle's novel A Wrinkle in Time, the characters in the story travel through time and space using tesseracts. The book actually uses the idea of a tesseract to represent a fifth dimension rather than a four-dimensional object (and also uses the word "tesser" to refer to movement from one three dimensional space/world to another).

7. In the science fiction novel Factoring Humanity by Robert J. Sawyer, a tesseract is used by humans on Earth to enter the fourth dimension and contact another civilization on a planet orbiting the star Alpha Centauri A. The hypercube initially exists as a series of connected 3-dimensional cubes, which represent a hypercube that has been unfolded. Refolding the cube in a certain specific manner causes the reformation of the hypercube in 4 dimensions.

8. In John Mighton's play, Half Life, one of the characters (an aging mathematician) builds a tesseract (or rather, the projection of a tesseract) out of popsicle sticks. In the Season 1 episode "Rampage" of the television crime drama NUMB3RS, main character mathematician Charlie Eppes discovers a popsicle-stick tesseract (projection) he built as a boy.

9. If you are bored with 3D Rubik's cube, you can try your hands on Rubik's tesseract like shown in this video

10. Mathematically, "time" is not "the fourth dimension"; "space time" is a particular physical model, but in mathematics, 4-dimensional Euclidean space is simply the set of all ordered 4-tuples (a,b,c,d)(a,b,c,d) with a,b,c,da,b,c,d real numbers, satisfying certain axioms. Time doesn't enter into it. Arturo Magidin's comment at math.stackexchange.com

**References**:1. Wikipedia

2. Cut The Knot!

3. Wolfram Mathworld

4. The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover

### Simple math trick : Multiplying two numbers that differs by a small even number

This trick only works if you've memorized or can quickly calculate the squares of numbers. If you're able to memorize some squares and use the tricks described later for some kinds of numbers you'll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6.

Let's say you want to calculate 12x14.

When two numbers differ by two their product is always the square of the number in between them minus 1.

12x14 = (13x13)-1 = 168.

16x18 = (17x17)-1 = 288.

99x101 = (100x100)-1 = 10000-1 = 9999

If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.

11x15 = (13x13)-4 = 169-4 = 165.

13x17 = (15x15)-4 = 225-4 = 221.

If the two numbers differ by 6 then their product is the square of their average minus 9.

12x18 = (15x15)-9 = 216.

17x23 = (20x20)-9 = 391.

Source : wildaboutmath.com

Let's say you want to calculate 12x14.

When two numbers differ by two their product is always the square of the number in between them minus 1.

12x14 = (13x13)-1 = 168.

16x18 = (17x17)-1 = 288.

99x101 = (100x100)-1 = 10000-1 = 9999

If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.

11x15 = (13x13)-4 = 169-4 = 165.

13x17 = (15x15)-4 = 225-4 = 221.

If the two numbers differ by 6 then their product is the square of their average minus 9.

12x18 = (15x15)-9 = 216.

17x23 = (20x20)-9 = 391.

Source : wildaboutmath.com

### Simple Math trick : Multiplying by 9, or 99, or 999

Multiplying by 9 is really multiplying by (10-1).

So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81.

Let us try another example: 56x9 = 56x10-56 = 560-56 = 504.

Isn't it simple enough.

To multiply by 99, you multiply by 100-1.

So same principle, 56x99 = 56x(100-1) = 5600-56 = 5544.

Same applicable for 999,9999 and so on.

So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81.

Let us try another example: 56x9 = 56x10-56 = 560-56 = 504.

Isn't it simple enough.

To multiply by 99, you multiply by 100-1.

So same principle, 56x99 = 56x(100-1) = 5600-56 = 5544.

Same applicable for 999,9999 and so on.

## Saturday, July 16, 2016

### Sultan math joke

For Indian Fans:

बेबी को Base पसंद है।

ये सुन के Hypotenuse और Perpendicular का दिल टूट गया।😂

बेबी को Base पसंद है।

ये सुन के Hypotenuse और Perpendicular का दिल टूट गया।😂

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