a good end of term task - if not used elsewhere
looking at a mixture of (2D representations of) some solids
powerpoint
and some complex solids
powerpoint: potatoes
it is relatively easy to prove that Euler's rule is true for any prism
and also any anti-prism
powerpoint: prisms (and anti-prisms)
it is also relatively simple to prove that Euler's relationship is true for any pyramid
and dipyramid
powerpoint: pyramids and dipyramids
although Euler wasn't the first to develop the rule that has his name, he did attempt an interesting proof, by induction: the relationship works for a resulting basic shape (the tetrahedron) following a collapse and at all stages of all options when progressively 'collapsing' a solid
this proof was later shown to be flawed but is still interesting
powerpoint: Euler's rule
the idea behind Euler's attempted proof by induction
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