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An Unexpected Right Angle
Bayes' Theorem
Circle as a limit of polygons
Circles of Apollonius
Combining Numbers
Complex logarithm
Constructing the square root
Cube roots, branch cuts, and Wolfram Alpha
Domain and Range
Eight Queens
Ellipse in a Box
Equilateral triangle and regular 9gon
Eratosthenes measures Earth
Hinged squares
Lights Out
Logarithmic Spirals and Exponentiation
Math Video Sites
Missing square puzzle
Parabolas through three points
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Equilateral triangle and regular 9gon
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This is a contest problem from the
AMC 12
, a mathematical contest for 12th grade students in the United States.
Given a ninesided regular polygon, how many distinct equilateral triangles in the plane of the polygon have at least two vertices on the polygon?
This GeoGebra applet can be used to visualize the problem. Can you find the solution?
equilateral triangle and regular 9gon.ggb
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Given a ninesided regular polygon, how many distinct equilateral triangles in the plane of the polygon have at least two vertices on the polygon?
This GeoGebra applet can be used to visualize the problem. Can you find the solution?