matthen

Things of interest in Maths & Science

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You can get interesting star patterns by joining up pairs of points along a circle, separated by a fixed angle. But if you imagine you are actually joining up one circle to another sitting below in the third dimension, you are actually creating a wireframe of a hyperboloid. [code] [more]

You can get interesting star patterns by joining up pairs of points along a circle, separated by a fixed angle. But if you imagine you are actually joining up one circle to another sitting below in the third dimension, you are actually creating a wireframe of a hyperboloid. [code] [more]

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Spinning a cube along a diagonal gives an interesting shape, composed of two cones and a curved part whose cross-section is a  hyperbolic curve. [more] [more2] [code]

Spinning a cube along a diagonal gives an interesting shape, composed of two cones and a curved part whose cross-section is a  hyperbolic curve. [more] [more2] [code]

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If you drop two stones in a pond one after the other, then two sets of concentric circles will emanate from where they were dropped. The curve formed by their points of intersection happens to be a hyperbola, this is the same type of curve which forms the shape of light cast on a wall by a lamp.  What would the curve look like if you dropped the stones at the same time? [more] [code]

If you drop two stones in a pond one after the other, then two sets of concentric circles will emanate from where they were dropped. The curve formed by their points of intersection happens to be a hyperbola, this is the same type of curve which forms the shape of light cast on a wall by a lamp.  What would the curve look like if you dropped the stones at the same time? [more] [code]

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Transforming from ellipses to hyperbolas, by considering slowly changing the equation   (a circle) into the equation  a (hyperbola). The purple lines represent different ‘radiuses’. I’ve been a bit obsessed with conic sections recently! [code]

Transforming from ellipses to hyperbolas, by considering slowly changing the equation   (a circle) into the equation hyperbola a (hyperbola). The purple lines represent different ‘radiuses’. I’ve been a bit obsessed with conic sections recently! [code]

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This morning I looked at my lamp, and wondered what curve it was projecting on the wall. I did some maths, and figured out it was a hyperbola.  This is nice, as it gives you a geometrical idea of how a hyperbola can be created- just project from a bulb in the middle of a lamp shade to a wall! I made this animation to show how the curve changes as the lamp does. Can you see why the curve tends to a straight line on either side? [mathematica code]   [more]

This morning I looked at my lamp, and wondered what curve it was projecting on the wall. I did some maths, and figured out it was a hyperbola.  This is nice, as it gives you a geometrical idea of how a hyperbola can be created- just project from a bulb in the middle of a lamp shade to a wall! I made this animation to show how the curve changes as the lamp does. Can you see why the curve tends to a straight line on either side? [mathematica code]   [more]

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French curves were used in manual drafting to draw curves of various shapes. In general you would plot various known points on the paper, and seek to join them up on the edge of a French curve.  But why are they the shape they are?  The one on the top left is meant to be good for hyperbolas, top right for ellipses, and the big one for parabolas (all the conic sections except the circle, which can be drawn easily anyway).  Are these shapes somehow optimal for drawing curves? I can’t find any maths to support this.
Feynman did note this property: “the French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.” This is a joke, as all smooth curves have this property. [more]  [read this book!]

French curves were used in manual drafting to draw curves of various shapes. In general you would plot various known points on the paper, and seek to join them up on the edge of a French curve.  But why are they the shape they are?  The one on the top left is meant to be good for hyperbolas, top right for ellipses, and the big one for parabolas (all the conic sections except the circle, which can be drawn easily anyway).  Are these shapes somehow optimal for drawing curves? I can’t find any maths to support this.

Feynman did note this property: “the French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.” This is a joke, as all smooth curves have this property. [more]  [read this book!]

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Yum! A pringle is a hyperbolic paraboloid; a ‘double saddle’ shape, the same shape kind of shape as a ridge connecting two mountains. Remember, hyperbolas are really, really, really awesome!!! [more] [code]

Yum! A pringle is a hyperbolic paraboloid; a ‘double saddle’ shape, the same shape kind of shape as a ridge connecting two mountains. Remember, hyperbolas are really, really, really awesome!!! [more] [code]

Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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