Malfatti: Trig supplement
- Author:
- Ryan Hirst
The following trigonometric expression arises in Malfiatti's problem
But this is an equality I know, in a very frumpy disguise. Let me find it.
That is, this expression says α+β = λ.
But
An exterior angle of a triangle is equal to the sum of its two opposite, internal angles.
I may draw λ as the external angle of a triangle, with opposite internal angles α, β. And the knot at the heart of Malfatti's problem is undone.
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Malfatti's Problem:
1. Describe the constraints: http://www.geogebratube.org/material/show/id/32079
2. Solution http://www.geogebratube.org/material/show/id/32233
→3. Trig Supplement
This is problem # 30 in Heinrich Dorrie's 100 Great Problems of Elementary Mathematics.
More: (http://www.geogebratube.org/material/show/id/73813)