Difference between revisions of "User:Bobthesmartypants"

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-==Problems==
-'''Problem 1''' <asy>
-draw(Circle((0,0),1));
-for (int i = 0; i < 10; ++i){
-  draw((0,0)--dir(360/(2^i)-90));
-}
-</asy>
-A unit circle is divided into halves. One half is divided into two halves again, and one of those is divided again, and so on. Each of these sectors of the circle is rolled up into a cone, and a circular base is capped onto each one. what is the combined surface area of all of the cones?
-'''Problem 2''' Let <math>r_1,r_2,\ldots r_{2014}</math> be rational numbers, <math>z_1,z_2,\ldots z_{2014}</math> be integers. Prove that <math>\displastyle\sum_{i=1}^{2014} z_i\cdot \text{arctan }r_i</math>, given that it is defined, can be expressed in the form <math>\text{arctan }r'</math>, where <math>r'</math> is a rational number.

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