Category Archives: Miscellaneous

A discussion forum

In order to facilitate discussion, I have set up a discussion forum here: http://cuhkmath.606h.net/phpBB3/viewforum.php?f=2 One of the most effective way of learning mathematics is by discussion. While there are excellent sites like MathOverflow or StackExchange where you may even find … Continue reading

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Why does a mirror reverse left and right, but not top and bottom?

If you stand in front of a mirror and raise your right hand, it appears in the mirror that you raise your left hand. Why does a mirror reverse left and right, but not top and bottom? For some of … Continue reading

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The 10th Taiwan Geometry Symposium

This is not really a “mathematical” post. Since this is the first symposium I’ve ever co-organized, I am supposed to advertise it (a bit). So if you happen to be in Taiwan, and are interested in geometry (OK, I know … Continue reading

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High degree polynomial with few real roots

There are univariate polyomials that the number of non-real roots is significantly larger than that of real roots. The simplest example is where is odd. It has one real root and non-real roots. In this post we show an example … Continue reading

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Two little remarks on sphere

1. “Take a sphere of radius in dimensions, large; then most points inside the sphere are in fact very close to the surface.” David Ruelle Let and . Let The fraction of the volume of to the volume of is … Continue reading

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Mathematics behind JPEG

Many of you should have this experience: when you save a picture with many words in Paint(小畫家) as .jpg file, some ugly artifacts appear. Then you may think why is such a low quality image format so common? At the … Continue reading

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On integrating products of dot products

Today KKK showed me the following formula: There exists a constant such that for all . Here the integral is either over the unit sphere or over the ball (of course the corresponding constants are different). In this note we … Continue reading

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