Euclid's Muse

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Search Results for “Crop-circles”

By Phil Todd
Ellipse as locus of circle center
Take two overlapping circles.  Examine the locus of the center of the circles tangential to both. It seems to be an ellipse with foci at the centers of the two circles. Prove it.

Tags: ellipse, conic, focus

By Phil Todd
September Problem
The radii of the small circles add up to that of the large circle. Why?

Tags: incircle, triangle

By Nick Halsey
Twisted Savonius Wind Turbine Full Geometric Model (without traces/surfaces)
The Twisted Savonius Wind Turbine has promising applications for rooftop usage, but its high cost has kept it unfeasible for widespread adoption. The Twisted Savonius Geometric Modeling project explored the geometric properties of the turbine's shape, and proposed a more efficient method of construction and geometric design as a result. This is the complete side view "3d" model of the turbine. It models an extremely 3-dimensional shape by using ellipses to represent tilted circles. Changing X changes the rotation of the turbine (in operation). Theta represents the twist angle between the top and the bottom of the turbine. T controls the parametric location of the vertical surface - tracing it "fills in" the blade's surface. Learn more about this side view model. Visit the Geometry of the Twisted Savonius Wind Turbine website.

Tags: Twisted-Savonius, Wind-Turbine, Pseudo-3d, Model, Geometric, Real-World, Ellipses, Arcs, Loci

By Andrew Zhao
Euclids Elements - Book 1 - Proposition 01
The very first proposition, in which Euclid creates a equilateral triangle from a straight line by using two circles.

Tags: Euclid, Elements, Geometry, Equilateral, Triangle

By Phil Todd
proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.

Tags: ellipse, focus


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