(no subject)

[simont]

Hmmm. While contemplating my previous entry about little things not typically making me either any happier or any less happy, I seem to have accidentally proved a theorem in geometry. Oddly this has made me happier, because geometric theorems are shiny :-)

(Consider a polygon, and a point moving around inside it. Consider the sum of the shortest distances from the point to each side of the polygon. Theorem: if the polygon is regular, then this sum remains completely constant no matter where the point moves inside it. Proof, and relevance to my emotional life, left as exercises for the reader…)

Comments

[ex-lark-asc.livejournal.com]

I don't like exercise, do you deliver enlightenment locally? :)

[(Anonymous)]

You must mean the sum of the perpendiculars from the point to the lines *extending* the sides of the polygon.

[simont]

Quite right; sorry.

[rmc28]

Ah, so to change the distance, you need to change the sided-ness of your polygon. Or change the shape of it, so moving around has an effect.