# Search Results for “right-triangle”

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

Tags: equilateral, triangle, Euclid

By Duncan
##### Triangle Areas
Can you triangles with integer side lengths and integer area?

Tags: triangle, area

##### 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.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle

##### 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?

Tags: maximum-area

##### 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

##### 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.

Tags: parabola, Archimedes

##### 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.

Tags: Euclid, Elements, Geometry, Pentagon, Triangle

By Duncan
##### 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.

Tags: ellipse, focus

##### Euclids Elements - Book 1 - Proposition 45
Creating a parallelogram equal to a given quadrilateral with a given angle.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle, Angle

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

Tags: incircle, triangle