How to Make a Yoshimoto Cube

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The following is a tutorial about how to make the Yoshimoto cube using paper (though it takes a very long time!). To make it you’ll need paper, scissors, some glue, and some adhesive tape.

How to Make a Yoshimoto Cube origami

You can check out a non-paper version here.

To make one yourself you can print out the following Yoshimoto sheet and try to assemble it yourself 🙂

Top ln(e^10) reasons why e is better than pi

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10) e is easier to spell than pi.
9) Pie without e just doesn’t taste that good.
8) The character for e can be found on a keyboard, but pi sure can’t.
7) Everybody fights for their piece of the pie.
6) ln(pi) is a really nasty number, but ln(e) = 1.
5) e is used in calculus while pi is used in baby geometry.
4) ‘e’ is the most commonly picked vowel in Wheel of Fortune.
3) e stands for Euler’s Number, pi doesn’t stand for squat.
2) You don’t need to know Greek to be able to use e.
1) You can’t confuse e with a food product.

The 5 Pirates Puzzle

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Five pirates (of different ages) have a treasure of 100 gold coins. On the ship, they decide to split the coins using the following scheme:

  • The oldest pirate proposes how to share the coins, and all pirates remaining will vote for or against it.
  • If
    50% or more of the pirates vote for it, then the coins will be shared
    that way. Otherwise, the pirate proposing the scheme will be thrown
    overboard, and the process is repeated with the pirates that remain.

Assuming
that all five pirates are intelligent, rational, greedy, and do not wish
to die, what should the oldest pirate propose to a) survive and b) maximize his profit?

pirate skull cross bones

(x, why?) Comics – All about math!

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(x, why?) Comics is a geeky and hilarious comic about math. It is created by Chris Burke, a high school math teacher in New York as well as a part-time writer, and a fan of science-fiction / fantasy books and films.
He started making his own math webcomic totally by accident as a way of
amusing his students and trying to make them think just a little bit
more.

You can check out over 300 geeky comics at: xwhy.comicgenesis.com

Prime number trick (with solution)

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Using prime numbers, you can amaze your friends with a prime prediction…

1. Ask your friends to pick any prime number greater than 3.
2. Square it.
3. Add 14.
4. Divide by 12.

Without knowing which prime number your friends picked, you can still tell them:
    There will be a remainder of 3.
But HOW does it work?
Let’s do an example:
13 is a prime number, squaring it gives 169, adding 14 gives 183 which has a remainder of 3 upon division by 12.

This works for every prime number greater than 3, but how exactly does it work?

The mathematics behind this is rather simple.
1. Let p be a prime number, p > 3.
2. Squaring gives:
    p^2.
3. Adding 14 gives:
    p^2 + 14
4. Taking it modulo 12 gives:
    (p^2 + 14) mod 12

We want to show that:
    (p^2 + 14) mod 12 = 3
This is equivalent to:
    p^2 – 1 is divisible by 12.
That is:
    (p-1)(p+1) is divisible by 12.

For a number to be divisible by twelve, it has to be divisible both by 3 and by 4. We know that, out of p-1, p and p+1, one of them must be
divisible by 3; and it can’t be p, because p is prime and greater than 3. Thus, either p-1 or p+1 is divisible by 3, and so their product is also:
    (p-1)(p+1) is divisible by 3.

Now, since p is a prime greater than 3, we know that it is odd. Therefore, both p-1 and p+1 are even numbers. The product of two even numbers is divisible by 4, so:
    (p-1)(p+1) is divisible by 4.

Combining this with the above, we get that:
    (p-1)(p+1) is divisible by 12.
And hence:
    (p^2 + 14) mod 12 = 3

I know 50

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Daniel would like you to know that he knows 50 digits of pi. He uses groups of 5:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

This is all he knows and he is going to see how far he can get!

Thanks to Daniel Dercksen for this submission!

Your shoe size can tell your age?

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398223_377175825696253_1241374619_n

I. Input shoe size

II. blah

III. blah

IV. blah

V. blah (Arbitrary number that makes this work, but only for the year 2012)

VI. Input age

Output is your shoe size and age. If you input someone else’s values, it outputs their values back. Magic!

Thanks to Nick de Vera for this submission!