# Search Results for “triangle”

##### Equilateral triangle construction

How Euclid constructs an equilateral triangle, using just a set of compasses.##### Euclids Elements – Book 1 – Proposition 42

To construct, in a given rectilineal angle, a parallelogram equal to a given triangle. In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.##### Maximum Area Triangle

The app uses a physical model to find the largest area triangle whose vertices lie on a smooth closed curve (defined by the red control points). The triangle defined by the tangent lines at the vertices is displayed, along with its medians. What do you notice about the maximum?##### Focal Triangle

Create a triangle which has 3 points on the circumference of an ellipse, and two sides passing through the foci. Look at 2 curves formed by the third side: the locus of its center and its envelope. One is an ellipse, the other is not.##### Tangent Triangle

We show the areas of the triangle formed by joining 3 points on a parabola, and that formed by the tangents to the parabola at those points.##### 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.##### Euclids Elements – Book 4 – Proposition 11

Can you create a regular pentagon without a protractor? Because it’s pretty impressive how Euclid did it with only a compass and a ruler. Note that the yellow triangle is similar to the one inside the pentagon.##### Epic Circle Trace 2

A triangle, defined by three points that are located proportionally around a circle by functions of*t*, is traced as

*t*varies from 0 to 2Π. What are the functions of t, f(

*t*), g(

*t*), and h(

*t*), that define the points D, E, and F, respectively?

*Hint: one of the functions is _(t) = t.*