Parabolic segment area
- Author:
- Cristina Chiusa
- Topic:
- Area
A parabolic segment is the region bounded by a parabola and line. To find
the area of a parabolic segment, Archimedes considers a certain inscribed
triangle. The base of this triangle is the given chord of the parabola, and the
third vertex is the point on the parabola such that the tangent to the
parabola at that point is parallel to the chord.
Move points A and B and look at the values of the areas.
The blue triangle area is always 1/8 of the red one and the green triangle area is 1/8 of the blue one!