# You're reading: Posts Tagged: Geometry

It’s Friday again! And with a seamless unbroken chain of Follow Friday posts stretching backward through time with no discernible gap, here’s another post with some recommendations of people to follow on Twitter if you’re into maths.

(At last month’s big MathsJam conference, we asked a few people who gave particularly interesting talks if they’d like to write something for the site. A surprising number said yes. First to arrive in the submissions pile was this piece by Tom Button.)

The formula for the surface area of a sphere, $A=4\pi r^{2}$, is the derivative of the formula for the volume of a sphere: $V=\frac{4}{3}\pi r^{3}$.

This result does not hold for a cube with side length $a$ if the surface area and volume are written in terms of $a$. However, if the surface area and volume are written in terms of half the side length, $r=\frac{a}{2}$, you get the surface area $A=24 r^{2}$, which is the derivative of the volume, $V=8 r^{3}$.

### 11-category Venn diagram drawn

Little known fact: some sized Venn Diagrams have never been drawn. In case you missed it when it whipped round Twitter a few weeks ago: it looks like someone finally cracked the 11-Venn diagram, and it’s a cracker!

### Bill Thurston has died

William Thurston died yesterday of cancer, aged 65.

Thurston was one of the greatest contemporary mathematicians; a huge figure in low-dimensional topology. I won’t bother writing out a mathematical biography – Wikipedia and MacTutor have all the relevant information, as usual, and I won’t pretend I know a huge amount about the exact details of Thurston’s achievement. Instead, I’ve tried to gather together a few links from around the web that give an idea of why Prof Thurston was so widely admired.

### Ask a mathematician: “Where should we live?”

Dear Mathematician,

My partner and I are trying to buy a house. We both work in different places, and neither of us enjoys commuting. How could we decide where to live?

Fictionally yours,

Norman Mettrick

Norman,

Thank you for your intriguing and entirely imaginary letter. The short and not terribly useful answer would be:

### In what flipping dimension is a square peg in a round hole just as good as a round peg in a square hole?

In what flipping dimension is a square peg in a round hole just as good as a round peg in a square hole?

Let’s start at the beginning.

My Plus magazine puzzle from March asks “Which gives a tighter fit: a square peg in a round hole or a round peg in a square hole?” By “tighter” we mean that a higher proportion of the hole is occupied by the peg.