#Pick a number between 1 and 3 quote download#

We can check it as follows:ДЈ 2+4 2 = 9 + 16 = 25 = 5 2 so a 2 + b 2 = h 2. It is perhaps surprising that there are some right-angled triangles where all three sides are whole numbers called Pythagorean Triangles.The three whole number side-lengths are called a Pythagorean triple or triad.ДЄn example is a = 3, b = 4 and h = 5, called 'the 3-4-5 triangle'.

#Pick a number between 1 and 3 quote download#

There is a very nice illustration of A Device That Illustrates Pythagoras' Theorem that is a Mathematica Demonstration.Click on the image on the right here to see an animation in a new window or to download the active controls version usable with the free Mathematica player.Д«ill Richardson has a nice animation of Bhaskara's proof The 3-4-5 TriangleIn the example above, we chose two whole-number sides and found the longestside, which was not a whole number. Don't turn them or flip them, just move themto their respective corners. This makes an effective visual aid by pushing the squares from their locations on the left towhere they are shown on the right. So the two blue squaresare equal in area to the red square, for any right-angled triangle: a 2 + b 2 = c 2 This does not depend on the lengths a, b, c only that they are the sides of a right-angled triangle. The left square also has two blue squareswith areas a 2 and b 2whereas the right hand one replaces them with one red square of area c 2. Is called a Pythagorean triangle Some visual proofs of Pythagoras' Theorem My favourite proof of the look-and-see variety is on the right.Д«oth diagrams are of the same size square of side a + b.Д«oth squares contain the same four identical right-angled triangles in white (so it is white-angled )with sides a, b, c. On this page, a triangle with a right-angle (so that Pythagoras' theorem applies)ДЄnd whose sides have lengths which are whole numbers If the longest side is h, then, by Pythagoras' Theorem, we have: If it equalled the sum of the other two then the triangle is just a line of length a + b = h!ДЇor example, if the two shorter sides of a right-angled triangle are 2В cm and 3В cm, what is the length of the longest side? Note that in any triangle, the longest side h cannot be longer than the sum of the other two sides.so h < a + b.

If all the angles of a triangle are less than 90В° then h 2 a 2 + b 2.

H 2 = a 2 + b 2 is only true for right-angled triangles. The square of the longest side is the same as the sum of the squares ofthe other two sides. If the longest side (called the hypotenuse) is h and the other two sides (next to the right angle) are called a and b, then: 90В°) then there is a special relationship between the lengths of its three sides: He is known to most people because ofthe Pythagoras Theorem that is about a property of all triangles with a right-angle (an angle of 90В°): If a triangle has one angle which is a right-angle (i.e. He was interested in mathematics, science and philosophy. Right-angled Triangles and Pythagoras' Theorem Pythagoras and Pythagoras' TheoremPythagoras was a mathematician born in Greece in about 570 BC. Please direct any criticism of the graph (e.g.Contents of this page The icon means there is a Things to do section of questions to start your own investigations.The calculator iconindicates that there is a live interactive calculator in that section. More interestingly, however, the top result implies that, given the choice, more people seem to prefer a 69 to anything elseвЂ¦ДЄnyway, it proves a point that IвЂ™ve made more than a few times on this blog, namely that people generally have a very poor idea of what randomness is and are particularly bad at making random choices or generating random sequences.

And I suppose 77 is an extension of that.

ItвЂ™s well known amongst purveyors of conjuring tricks and the like that if you ask people to pick a number between 1 and 10, far more people choose 7 than any other number. The most popular picks are in fact 69, 77 and 7 (in descending order). You might naively expect the histogram to be flat (give or take some Poisson errors), consistent with each number having the same probability of being picked, but there are clearly some numbers that are more likely to be chosen than a constant probability would imply. The graph shows the results obtained when 6750 people were asked to pick an integer `at randomвЂ™ between 1 and 100. I saw this circulating on Twitter and thought I would share it here it was originally posted on reddit.