Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.
We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.
An introduction to some beautiful results in Number Theory.
