# BRayTracer Version 0.8 Released!

I’ve been having some very bad back pain today, and so today took some time off from work and class (it was the first day today!) to lay in bed and work on finishing up version 0.8 of BRayTracer.

I’m very proud of the improvements I’ve made to the latest version. Usability has been increased significantly and there are probably over a hundred bug fixes.

# Math can be freaky…

To preface, I am not a mathematician. I can hold my own in most college-level math (I’ve taken 3 years of algebra, trig, geometry, 3 years of calculus, and 1 year linear algebra: where is all that knowledge now?), but I’m still easily impressed.

I’ve been working through an algorithm textbook (more on that later), which mentions a number of very interesting mathematical equalities:

I.
13 = 1
23 = 3 + 5
33 = 7 + 9 + 11
43 = 13 +15 + 17
etc.

II.
13 + 23 + … + n3 = (1 + 2 + … + n)2

III.
12 = 1
22 = 1 + 3
32 = 1 + 3 + 5
42 = 1 + 3 + 5 + 7
etc.

To be honest, when I first read these it blew my mind. There is a beautiful correspondence demonstrated in these ancient forumlas that is nearly breathtaking when you first learn of them.