# Euclid's Muse

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# Search Results for “triangle”

##### Minimum Perimeter Inscribed Triangle
Three masses are constrained to lie on the edges of a triangle.  Equal constant force actuators (with force F) are attached to each pair of masses.  When this system finds equilibrium, the potential energy will be at a minimum.  However, the PE in each actuator is simply F times L, where L is the length of the actuator. Hence minimum PE is achieved when the masses sit at the vertices of the minimum perimeter inscribed triangle. Press Show to see the normals to the sides of the triangle at the location of the masses.

Tags: Fagnano, altitude, triangle

##### Largest Outscribed Equilateral Triangle
Drag A,B, C to change the original triangle.  Press Play to watch a spring driven equilateral triangle gradually settle at the maximum perimeter position. Press Show to see the perpendiculars to the sides of the equilateral triangle through A, B and C. Note that the mechanism settles at a position where these perpendiculars are concurrent. This is a problem from The Mathematical Gazette March 2014 pp 79-84.

Tags: Fermat, toricelli, equilateral, triangle

##### A triangle from medians
AD, BE and CF are medians of the triangle ABC. Triangle GHI has GH=BE, HI=CF and GI=AD. HL, IJ and GK are medians of GHI. What is the relationship between the length of these medians and the lengths of the sides of ABC? Can you prove this relationship geometrically?

Tags: triangle, median

##### Area of a Triangle
This app allows you to compare areas of an arbitrary triangle and a parallelogram in order to discover the formula for the area of the triangle.

Tags: area, triangle

##### Minimum Perimeter Triangle
Constant force actuators pull the masses and remain tangent to the curve.  Potential energy for these actuators corresponds to their length.  Hence a minimal energy configuration should minimize the perimeter of the triangle. Press Show to see the cevians to the points of contact with the curve. Pres Show a second time to see the normals at the points of contact. What do you notice?

Tags: Cevian, triangle, curve, minimum, perimeter

##### Equilateral triangle construction
How Euclid constructs an equilateral triangle, using just a set of compasses.

Tags: equilateral, triangle, Euclid

##### Maximum Area Triangle
A force proportional to the length of each side are applied to the side's midpoint.  This models a constant pressure, and potential energy should be minimized when area is maximized. Press Show to see the tangents to the curve at the points of contact. What do you notice? You can change the definition of the curves, but be careful, or the masses might escape!

Tags: maximum, triangle, area

By Marissa
##### Example: Euclid's Equilateral Triangle
From "Creating HTML5 Apps with Geometry Expressions." Download the GX file to see how this app was made.

Tags: example, advance-button, visibility, euclid, equilateral-triangle

By Marissa
##### Triangle Support Reaction Assessment App
From "Creating HTML5 Apps with Mechanical Expressions."

Tags: example, triangle, forces, assessment

By Marissa
##### Example: Area of a Triangle
From "Creating HTML5 Apps with Geometry Expressions." Download the GX file to see how this app was made.

Tags: example, draggable, triangle, area