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The relationship between parabolas, hyperbolas, circles and ellipses is easy to see once they are understood as conic sections.
I think the relationship between geometric shapes such as squares, rhomboids and trapezoids could be taught in a similar way to conic sections as cross sections of polyhedra
(e.g. a pyramid).
All types of triangles (right angle, equilateral, isosceles, scalene) could be also be visualised as cross-sections of a single polyhedra (i.e. a triangular prism).
This could be used in educational videos or software.
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||Hmmm. I'm not entirely sure this would
be easier - it depends on which features of
the plane shapes you are trying to
illustrate. Can you give a specific
||visualising shapes in this way is easier and more interesting for me because I think in 3d rather than 2d.
||Also, shapes like trapezoids seem so... arbitrary. this puts shapes in some kind of context.
||Hmmm. You mean "slice this
dodecahedron this way and you get a
pentagon" type of thing? Fair enough, but
then you still have to learn about the
properties of the plane shape, once you've
found where it comes from.
||(+) Suddenly it all makes sense.
||I'll agree to it only as a supplement to the current system. There's no harm in offering the same information spun different ways since children have so many different learning styles.