Tag Archives: practical

Real problems with conic sections (ellipse, parabola)

So there is an oval hole in a metal casting. It’s supposed to be an elliptical hole. Is it ????? How can we find out ?????
A good start would be to find the line which would be the major axis if it was elliptical. This turns out to be an engineering problem, not a mathematical one (I cannot see a way!). If the oval curve has an axis of symmetry then the method below will find it:

Firstly, get a computer picture of the oval.
Take two circles, of different radii, and push them along until each one touches the oval in two places.

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The line joining the two centers will be the axis of symmetry if there is one (this can be shown mathematically).

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ellipse5

The equation of an ellipse uses the lengths of the major and minor axes. Do it !

The closeness to elliptic can be assessed in various ways. Think of one.

next…..finding the focus of a parabolic shape

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Filed under conic sections, conics, education, engineering, geometry, math, teaching

A “real life” geometry problem.

While designing a system for connecting “educational” cubes together I figured that the holes in the faces had to be positioned very carefully. To achieve what I wanted the holes had to be positioned with Ā length a equal to length b, and length c had to be twice the length a.

So what is length a, as a fraction of the side of the cube ?

geometry from real life
There will be eight holes altogether, and all cubes are the same size.

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Filed under education, geometry, teaching