By proving these particular identities, prove the existence of general cases.
Discover how networks can be used to prove Euler's Polyhedron formula.
Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?
Can the pdfs and cdfs of an exponential distribution intersect?
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
With n people anywhere in a field each shoots a water pistol at the nearest person. In general who gets wet? What difference does it make if n is odd or even?
