This applet shows the construction of a square with the same area as a given triangle.
Author: Irina Boyadzhiev of Ohio State University.
Download GGB File
Monday, January 16, 2012
Monday, January 9, 2012
Area of Triangles Under a Curve
Given: Right triangle BCD whose hypotenuse is tangent to the function f(x) = a/x.
- Move slider a and observe what happens? How is the appearance of the graph relate to a?
- Move point A and observe the triangle? What do you observe?
- What conjecture can you make based on your observation in 2. Prove your conjecture.
Thursday, January 5, 2012
Equation of a Circle
Move sliders h, k, and r to form the desired circle.
This applet shows that a circle can be determined given a center (h,k) and a radius r.
Download GGB File
This applet shows that a circle can be determined given a center (h,k) and a radius r.
Download GGB File
Monday, January 2, 2012
Routh's Theorem
Move ABC to determine the shape of a desired triangle and move the slider. What do you observe?
The Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the intersection of three cevians. The theorem states that if in triangle ABC points D, E, and F lie on segments BC, CA, and AB, then writing 
= x, 
= y, and 
= z, the signed area of the triangle formed by the cevians AD, BE, and CF is the area of triangle ABC times
= x, = y, and = z, the signed area of the triangle formed by the cevians AD, BE, and CF is the area of triangle ABC times
This theorem was given by Edward John Routh on page 82 of his Treatise on Analytical Statics with Numerous Examples in 1896.
Source: Wikipedia
Download GGB file
Source: Wikipedia
Download GGB file
Subscribe to:
Posts (Atom)