145 = 1! + 4! + 5!
1! = 1
4! = 4*3*2*1 = 24
5! = 5*4*3*2*1 = 120
120 + 24 + 1 = 145
Showing posts with label math(ish). Show all posts
Showing posts with label math(ish). Show all posts
Tuesday, October 11, 2011
Wednesday, June 8, 2011
The parity of 0
Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. Coincidentally an even parity is denoted parity 0. Therefore it is true that 0 has parity 0.
Zero fits the definition of an even number: An even number is an integer of the form n = 2k where k is an integer. It also exhibits all properties shared by all even numbers, including but not limited to:
- being divisible by 2
- being surrounded on both sides by odd integers
- able to be split into two equal groups
Zero also fits the rules for sums and products of even numbers, such as even − even = even, so any alternate definition of "even number" would still need to include zero.
More: Wikipedia
Thursday, June 2, 2011
Is π any good beyond 39 decimal places?
It has been said that π truncated to 39 decimal places is sufficient to estimate the circumference of any circle that fits in the observable universe with precision comparable to the radius of a hydrogen atom.
Back of the envelope time:
The observabe universe has a diameter of about 93 billion light years or 8.79873*10^26m. The circumference of the observable universe (assuming that it is spherical in shape) is therefore π*8.79873*10^26m or about 2.76420*10^27m. An error in π of +/-1.0*10^-39 would result in an error in the circumference of something on the order of +/-1.0*10^-12m (very roughly). The average orbital radius of H is about 5.29177*10^-11m.
So, Is π any good beyond 39 decimal places (even though it has an infinite decimal expansion)?
Answer: Probably not other than for theoretical and computational interests.
So, Is π any good beyond 39 decimal places (even though it has an infinite decimal expansion)?
Answer: Probably not other than for theoretical and computational interests.
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