Category Archives: Geometry/Topology

Can computers write proofs

Posted on 8/4/2013 by tpc

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 →

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Geometry Puzzle

Posted on 5/12/2012 by tpc

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

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Nice geometry problem

Posted on 27/9/2012 by tpc

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

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Dodecagon

Posted on 6/9/2012 by tpc

Funny cartoon from savage chickens.link

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A matter of perspective

Posted on 18/5/2012 by tpc

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

Posted on 5/5/2011 by tpc

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 →

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MAA and applications of topology

Posted on 3/9/2010 by tpc

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 →

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Origami and Mathematics

Posted on 20/7/2010 by tpc

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 →

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Picture Hanging Puzzle

Posted on 12/7/2010 by tpc

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

Posted on 14/6/2010 by tpc

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

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Klein Bottle Opener

Posted on 27/5/2010 by tpc

How cool is that! http://www.bathsheba.com/math/klein/klein_x1.html $78 though.

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Finite Projective Plane

Posted on 11/5/2010 by tpc

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

Posted in Combinatorics, Geometry/Topology | Leave a comment

One down, six more to go

Posted on 19/3/2010 by tpc

The first of the 7 Clay milliennium prize has been awarded. Sure it was a controversial one, but I guess it was fitting that the winner was one who didn’t want the million bucks. Money is not the ultimate prize … Continue reading →

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Bach’s canon on a moebius strip

Posted on 16/9/2009 by tpc

From boing boing, exactly what the title says.

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Euler’s Rotation theorem in 3D

Posted on 28/9/2008 by tpc

Any rigid body displacement where a point is fixed is equivalent to a rotation. I saw this neat proof from Don Koks’ Explorations in Mathematical Physics. By the hypothesis [tex] |Ar| = |r| \implies r^t A^t A r = r^t … Continue reading →

Posted in Books, Geometry/Topology, Linear Algebra | 1 Comment

Ipod and the Golden Ratio

Posted on 17/1/2007 by tpc

I gave a talk before on the golden ratio, so when I came across this blog entry Ipod and the golden ratio via Gooseania, I quickly saved this link in case I have to give the same talk again.

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The Four Pillars of Geometry

Posted on 13/2/2006 by tpc

By John Stillwell. I picked this up from the new arrivals counter at the library. The hyperbolic tessellation on the front cover was invitation enough for me. The book is about teaching geometry to undergrads from four different perspectives: 1) … Continue reading →

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Teaching Trigonometry

Posted on 24/4/2005 by tpc

The most difficult part of teaching trigonometry to kids (more specifically, pre-university and below) is proving trigonometric identities. Typically, the stronger students would relish the challenge, while the weaker would despair. Some of them would even question what is the … Continue reading →

Posted in Geometry/Topology, Quotes/People, Teaching | 2 Comments

Jordan Curve Theorem

Posted on 6/2/2005 by tpc

I’ve never seen the proof of this theorem, although it is mentioned in every advanced calculus and geometry/topology course that I’ve taken. What I’ve learnt recently is that it cannot be generalised to higher dimensions, and the Alexander’s Horned Sphere … Continue reading →

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