• If you had a wire as long as the circumference of the Earth and added just ten meters to it it would float 1.6 meters off the ground everywhere.
• If you could fold a piece of paper 42 times you would reach the moon and beyond.
• If you have 23 people in a room there's a 50% chance that two of them share a birthday. If you have 50 people in a room there's a 97% chance that two of them share a birthday.
• (1/2)+(1/4)+(1/8)+(1/16)+(1/32)+...=1
• An infinite surface area can enclose a finite volume.
• Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" It is to your advantage to switch your choice.
• 10! seconds is exactly six weeks.
• If you properly shuffle a deck of cards, chances are the order in that deck has never been seen before.

Any others you guys can think of?

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• If you could fold a piece of paper 42 times you would reach the moon and beyond.

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Ones like these demonstrate how bad we are at estimating how much/how many of something really is.

At just 10 folds, it's over 1,000 sheets thick.

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• If you had a wire as long as the circumference of the Earth and added just ten meters to it it would float 1.6 meters off the ground everywhere.

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Thats crazy! I had to draw it out in CAD to prove to myself it was right!

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• If you could fold a piece of paper 42 times you would reach the moon and beyond.

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Ones like these demonstrate how bad we are at estimating how much/how many of something really is.

At just 10 folds, it's over 1,000 sheets thick.

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Ever heard the rumor that you can't fold a piece of paper more than seven times? These guys put that to the test:

2:13 . . .(laugh/cry emoticon)

Benford's Law: the number 1 appears as the first digit 30% of the time in real world numbers. Benford's Law has been used to detect when data is forged.

The Harmonic Series converges to infinity. Many other infinity series converge to a number.

Mathematically speaking, most people's sexual partners have had, on average, more sexual partners than they have had. This is due to the effect that a single promiscuous sexual partner will have on the average. Same mathematical concept also applies to friends in general.

It might be impossible to construct a triangle with interior angles that add up to 180 degrees.

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• If you had a wire as long as the circumference of the Earth and added just ten meters to it it would float 1.6 meters off the ground everywhere.

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I love ones like this because I know it's correct. I understand the math that makes it correct.

But my brain still completely rejects it.

It reminds me of the Monty Hall problem.

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Why?

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So when I say construct, I'm talking in our reality. I can use euclidean geometry and construct a 180 degree triangle very easily but our universe and space-time itself doesn't really conform to euclidean geometry. The main qualm (and this introduces non-euclidean geometries) is of the parallel postulate. It's an postulate that euclid makes that may not be valid.

If you want to envision a triangle with interior angle sum greater than 180 degrees, imagine drawing a triangle on a baseball. Or less than 180 degrees, drawing it on a hyperbolic sheet.

Here's a picture to help out:



So it calls into the question of flatness.

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• If you could fold a piece of paper 42 times you would reach the moon and beyond.

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I'm having difficulty picturing this one.

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• 10! seconds is exactly six weeks.

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Can one of you #mathnerds help me out with this one?

The rest of those are pretty cool.

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10! seconds is exactly six weeks.

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Can one of you #mathnerds help me out with this one?

The rest of those are pretty cool.

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10s x 9s x 8s x 7s x 6s x 5s x 4s x 3s x 2s x 1s = 60sec/min x 60min/hour x 24hr/day x 7day/week x 6weeks

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• 10! seconds is exactly six weeks.
Can one of you #mathnerds help me out with this one?The rest of those are pretty cool.

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6 weeks = 6*7*24*60*60 seconds.

Let's prime factor everything.

6=2x3.
24=3x2x2x2.
60=2x2x3x5.

So 6 weeks = 2x3x7x3x2x2x2x2x2x3x5x2x2x3x5 seconds. Counting everything up we have

6 weeks = 2^8 x 3^4 x 5^2 x 7

Using one 2 and one 5 as ten this becomes

2^7 x 3^4 x 5 x 7 x 10.

Using two 3s as 9 this becomes

2^7 x 3^2 x 5 x 7 x 9 x 10.

Using three 2s as 8 this becomes

2^4 x 3^2 x 5 x 7 x 8 x 9 x 10.

Using a 3 and a 2 as 6 this becomes

2^3 x 3 x 5 x 6 x 7 x 8 x 9 x 10.

Using two 2s as 4 this becomes

2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10.

We can always multiply by 1

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 10!

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• 10! seconds is exactly six weeks.
Can one of you #mathnerds help me out with this one?The rest of those are pretty cool.

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6 weeks = 6*7*24*60*60 seconds.

Let's prime factor everything.

6=2x3.
24=3x2x2x2.
60=2x2x3x5.

So 6 weeks = 2x3x7x3x2x2x2x2x2x3x5x2x2x3x5 seconds. Counting everything up we have

6 weeks = 2^8 x 3^4 x 5^2 x 7

Using one 2 and one 5 as ten this becomes

2^7 x 3^4 x 5 x 7 x 10.

Using two 3s as 9 this becomes

2^7 x 3^2 x 5 x 7 x 9 x 10.

Using three 2s as 8 this becomes

2^4 x 3^2 x 5 x 7 x 8 x 9 x 10.

Using a 3 and a 2 as 6 this becomes

2^3 x 3 x 5 x 6 x 7 x 8 x 9 x 10.

Using two 2s as 4 this becomes

2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10.

We can always multiply by 1

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 10!

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Too late.

Bobo's explanation is much better than mine.

So I'm guessing the ! is a mathematical symbol?

You should follow up my non-euclidean rant with what Einstein did with it.

I'd be **** to explain it in a physics context.

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So I'm guessing the ! is a mathematical symbol?

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Yes. It's called a factorial, and means to multiply all positive integers up to a certain number. For instance 5!=1x2x3x4x5. 3!=1x2x3 and so on.

Also, 0! = 1 and 1! = 1.

Those definitions come in response to formulating permutations.

So when I see 10%!#$! that just means a mathematician is ticked off?

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It's the factorial operator.

n!=n*(n-1)*(n-2)...*2*1

So:
3!=3*2*1
5!=5*4*3!

Also, 0!=1 because we say so.

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I'd recommend reading chapter 3 of this isaac asimov book for a better explanation of 0!

It's a short 20 minute read.

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I want to add one more mathematical fact. I have debated this with more of my students than I wish to say:

(9/10)+(9/100)+(9/1000)+(9/10000)+...=1.

NOTE THE ****ING EQUALITY. IT'S NOT AN ALMOST EQUAL SIGN, IT'S NOT A IF YOU BELIEVE IT SIGN, IT'S A ******* EQUAL SIGN. ANYBODY WHO DISAGREES WITH ME ON THIS IN PERSON IS LIABLE TO GET STABBED.

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Wanna easy way to shut up your students?

An easy way to tell if 2 numbers are not equal is to state a number that exists between them.

If .99999... does not equal 1, then what number exists between them.

I've tried that. Lord knows I've tried. I've given simple proofs. I've given definitional proofs. I've given complex proofs. I've used every trick imaginable.They just refuse to believe me. HOW DO I REACH DEEZ KEEDS.

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I've tried that. Lord knows I've tried. I've given simple proofs. I've given definitional proofs. I've given complex proofs. I've used every trick imaginable.They just refuse to believe me. HOW DO I REACH DEEZ KEEDS.

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I can't help you there, I've left the teaching profession for good.

Now, I just worry about numbers having enough memory allocated in the heap.