Recent content by bruno C

This can be done with algebra after the problem has been restated. Note that the angle of a corner of a regular n-gon equals (n-2).Pi/n. To fit the plane, k copies of a regular n-gon must be able to touch with their corners and therefore k angles should make up for a total arc of 2.Pi...

Although the question is to help with induction, I thought I'd mention that sometimes induction is used but it is not necessary, in the sense that another proof exists that does not use induction. Why would it matter? Induction says something about an existing proof for all n. If you can...

It's not that hard to find three different Egyptian fractions that add up to 4/(4k+3). For any fraction of the form 4/(4k+3), compute the difference with the nearest integer fraction: 4/(4k+3) - 1/(k+1) = 1/((k+1).(4k+3)). If you are satisfied with the absence of 1/c you are ready...