Infinity is weird. Imagine an infinitely large, flat plane. Now imagine a pole of some height that holds up one end of another pole — one that stretches infinitely far.
If you were to let this infinitely long pole fall against the the ground, it would rest at precisely 90 degrees. That’s because if it were angle at all towards the ground, there would be a point some ways down the infinite pole that it would hit the infinite plane. Of course, you would never be able to see where it’s resting because of infinity and all, so instead, it would appear to float in mid-air.
From Futility Closet.
Cicadas emerge from the underground only periodically. Depending on the species, that period will be 7, 13, or 17 years, which are all prime numbers. Why does this make sense?
Suppose there are some predators (like birds, and the Cicada Killer Wasp) that attack cicadas, and that the cicadas emerge every 12 years. Then the predators that come out every two years will attack them, and so will the predators that come out every 3 years, 4 years and 6 years. But according Mario Markus, “if the cicadas mutate to 13-year cycles, they will survive.”
The other advantage is that cicada species with different intervals will rarely compete with each other for food.
Michael Hartl and Bob Palais want people to stop using pi and start using their constant tau (or τ). Tau is defined as the ratio of the circumference of a circle to its radius, while pi is the ratio of the circumference to the diameter. Hartl’s argument is that since the radius is a more important number for a circle than a diameter, the circle constant should rely on the more important number.
Did you know that 0.99999 (repeating) is the same number as 1? Here’s a simple proof:
- Let a = 0.9999…
- Multiply by 10: 10 * a = 10 * 0.9999…
- Simplified: 10a = 9.999…
- Subtract a: 10a – a = 9.999… – 0.9999…
- Which means: 9a = 9
- Divide 9: a = 1
- Voila: 0.9999… = 1
Of course, there’s always the simpler:
- 1/3 = 0.3333…
- Multiply by 3: 1 = 0.9999…
0 is the additive identity.
1 is the multiplicative identity.
2 is the only even prime.
3 is the number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
Special properties of numbers. I’ve only listed 1-10, but the list goes on and on and on.