# Category Archives: Geometry/Topology

## One-seventh ellipse

Fun fact. It is well known that $\frac{1}{7} = 0.\overline{142857}$. It turns out that if the repeating digits are taken in sequence as (x,y) pairs in the following manner to form six points: (1,4), (4,2), (2,8), (8,5), (5,7), … Continue reading

## Notes from ICME13

Gila Hanna mentioned the carpet proof of the irrationality of $\sqrt{2}$. A little digging reveals that it was due to Tennenbaum (1950s) and popularized by Conway (1990s). The original proof appeared in a book but the simple idea is described … Continue reading

## A Sunday Morning Geometry Problem

It’s 6.15 am on a Sunday morning, 18th October to be exact. The newspapers have not been delivered and the kids are still sleeping. Some peace and quiet for me to do some reading while sipping my morning coffee … … Continue reading

## Kobon Triangles

Students occasionally have great ideas. Was discussing a problem that originated from some students but was not very well posed. We managed to reformulate it as the maximum number of triangles that can be formed with n lines. This turns … Continue reading

## Come Together

is not the beatles song but the title of episode 16 of a tv program called discover science. I happened to catch it on local tv and the combination of quirky Japanese humour and the clever introduction to mathematics and … Continue reading

## Maths & Fashion

That headline caught my eye and earned the newspaper article a more detailed look. It’s about a sub brand from Issey Miyake called 132.5, which apparently stands for 1 piece of material which forms a 3d dress but yet can … Continue reading

## The broken stick problem

A slick solution to the broken stick problem or otherwise known as the uncooked spaghetti problem

## Polynomial Puzzle and Lill’s Method

I have in mind a polynomial with nonnegative integer coefficients. Can you determine completely the polynomial by just asking two questions? I forgot where I saw this from but it was interesting enough to spur a few lunch time discussions … Continue reading

## Can computers write proofs

that human being can understand? By that I mean not those formal logic nonsense. Tim Gowers is doing an interesting experiment to get readers to judge proofs of exercises in metric space theory. The three proofs are supposed to be … Continue reading

## Geometry Puzzle

A neat little puzzle from John Mason. How are the blue and red area related?

## Nice geometry problem

From the MAA minute math! a problem on 3d geometry. I must confess I peeped at the hint.

## A matter of perspective

Have you ever watched rugby matches on TV and noticed the advertisements on the field that looked 3-dimensional? I remember having the impression that the adverts were superimposed by the TV people. But when I told the wife, she plainly … Continue reading

Posted in Applications, Books, Geometry/Topology | 1 Comment

## Soap bubbles and current research

That’s the title of Frank Morgan’s talk today. The main takeaway is how, (motivated?) students can be exposed to interesting problems and work on current research. For example, it has been known for almost 2000 years that the circle in … Continue reading

## MAA and applications of topology

I used to be a member of MAA but found that it did nothing much for me except I get to issues of American Mathematical Monthly. I would classify that as good to have – something to read when I … Continue reading

## Origami and Mathematics

Recently I had the horrendous realization that I’ve lost whatever little origami skills that I once possessed. I was trying to entertain a bored child on the plane who speaks a little English, and I knew no German save “guten … Continue reading

## Picture Hanging Puzzle

Just attended a nice talk by Erik Demaine on Origami and puzzles. He demonstrated some remarkable stuff and ended with a cute picture hanging puzzle – how to hang a puzzle with two nails such that by removing either one, … Continue reading

Posted in Fun Stuff, Geometry/Topology | 1 Comment

## How Did Escher Do It

I’ve always loved Escher’s circle limit. Here’s a neat article attempting to reconstruct it.

Learned a cool trick today. The finite projective plane of order n has $n^2 + n + 1$ points, $n^2 + n + 1$ lines, $n + 1$ points on each line, $n + 1$ lines passing each point. The … Continue reading