Gabeland
Interesting math explorations
Category: Uncategorized
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This is a continued fraction: To evaluate it, just simplify from the bottom up. That one comes out to 225/157.For the rest of this, I’m going to use the following notation: 225/157 = [1,2,3,4,5].Each number has a unique continued fraction (as long as you don’t use 0), and the rational numbers all eventually terminate. But…
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First week of the new schedule! I already missed it. Anyways, take a basic six-sided die.You know, the one that has the numbers from 1 through 6 on it. Roll it twice, and add up the total.The result can be anywhere from 2 to 12, but it’s most likely to be 7. You can see…
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I thought of this as a potential math competition problem, but I think it’s better if I share it here!Consider the following setup:You have a circle of radius 1. Call it O. Two other circles of radius 1/2, A and B, are internally tangent to O and externally tangent to each other, like so: Now,…
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First, some background.The number of natural numbers (1, 2, 3, 4, …) and the number of integers (…, -2, -1, 0, 1, 2, …) are both infinite. But are they the same kind of infinite?The answer is yes, because you can match each integer to a natural number. Order the integers like this:0, 1, -1,…
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Let’s say we have a sequence, and we want to guess what polynomial generated it.For example:3, 10, 19, 30, 43, 58, 75, …Finite differences helps with determining that. How it works is, take the difference between each pair of terms.10 – 3 = 7, then 19 – 10 = 9, then 30 – 19 =…
Gabeland 