Fibonacci GCD's, please Fibonacci numbers exhibit striking patterns. Here's one that may not be so obvious, but is striking when you see it. Recall the Fibonacci numbers: n: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,... fn: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,... Now let's look at some of their greatest common divisors (gcd's): Teacher Portal - Sumdog's free maths games Sumdog > Sumdog's features > Games Sumdog's maths games are all free to play, whether you're at home or in school. (Why are they free?). 12 Dozen Places To Educate Yourself Online For Free All education is self-education. Period. It doesn’t matter if you’re sitting in a college classroom or a coffee shop. Intensity (physics) The word "intensity" as used here is not synonymous with "strength", "amplitude", "magnitude", or "level", as it sometimes is in colloquial speech. If a point source is radiating energy in all directions (producing a spherical wave), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to distance from the object squared. This is an example of the inverse-square law. Applying the law of conservation of energy, if the net power emanating is constant,
A Random Math Fun Fact! From the Fun Fact files, here is a Random Fun Fact, at the Advanced level: The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the divisibility of the integers. (It is often covered in calculus courses and begins by assuming Sqrt=x/y where x/y is in smallest terms, then concludes that both x and y are even, a contradiction. See the Hardy and Wright reference.) But the proof we're about to see (from the Landau reference) requires only an understanding of the ordering of the real numbers!
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Sums of Two Squares Ways In the Fun Fact Sums of Two Squares, we've seen which numbers can be written as the sum of two squares. For instance, 11 cannot, but 13 can (as 32+22). A related question, with a surprising answer, is: on average, how many ways can a number can be written as the sum of two squares? We should clarify what we mean by average. Let W(N) is the number of ways to write N as the sum of two squares. Thus W(11)=0, and W(13)=8 (as sums of squares of all possible combinations of +/-3 and +/-2 , in either order).
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15 Fun Science Activities for Kids We love fun science activities and science experiments. We have a whole list of fun ways to learn and explore today with your little scientist. These fantastic activities were inspired by Buggy and Buddy. 15 Fun Science Experiments for Kids 1. Odd Numbers in Pascal's Triangle Pascal's Triangle has many surprising patterns and properties. For instance, we can ask: "how many odd numbers are in row N of Pascal's Triangle?" For rows 0, 1, ..., 20, we count: