This n-gon (regular polygon of n sides) has a variable number of sides. Changing the value for n demonstrates very visually how regular polygons of increasing numbers of sides, with the same radius, have a shape that increasingly approaches that of a circle.
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?
Observe the definite integral of sine, or the area between the function sin(x) and the x axis, and how it changes between different bounds by dragging the boundaries, a and b. What happens to the area when the interval is 2Π? Why?
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.