Search Results for “Proof”
Proof by Shear Transformation
This app allows you to explore geometric proof that is a variation of the original Euclid’s proof. In this proof, the shear transformation is used to change the shapes without changing their areas.
Circle Proof
This is the first app ever on Euclid’s Muse! It provides a draggable diagram to help illustrate a mathematical proof. This proof was discovered when modeling the Twisted Savonius style wind turbine from a top view. The full proof can be found here.
Garfield's Proof
This app allows you to explore the algebraic proof offered by James A. Garfield, the twentieth president of the United States. He discovered this proof five years before he became the President.
Bhaskara’s Proof
This app allows you to explore algebraic proof by the ancient Hindu mathematician Bhaskara, who used the properties of similarity to prove the theorem.
Pythagoras' Proof
This app allows you to explore geometric proof offered by Greek mathematician Pythagoras himself.
proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.
Fermat Toricelli Geometric Proof
We use rotations to construct a path equal in length to the sum of the distances AE+BE+CE, whose end points are fixed. Minimum for AE+BE+CE occurs when this path is a straight line. So long as no angles of the original triangle are greater than 120 degrees, this works. What goes wrong when an angle does exceed 120 degrees?
Golden Section Construction
An illustration of Euclid's proof of how to construct a golden section, from Book 2, Proposition 11 of Euclid's Elements.
Chord Angle Theorem
The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth. Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn't change because of this theorem.
