Gradual Approximation (Video 2 of 7)

Gradual approximation (Yoshizawa) (2 of 7)

Students create parallelograms from a circle with pre-cut equal sectors of eight or 16 pieces.

A student (Yoshizawa; 00:10:31) explains a way of calculating the area based upon the formula for a parallelogram and translates this into a formula using circumference and radius. He goes further by explaining that using more pieces gives a better approximation to the area of the circle (1/2 circumference x radius).

The teacher calls upon other students to explain Yoshizawa's thinking. He later summarizes the students’ suggestions to increase the number of sectors; by doing so “it approximates a parallelogram gradually.”

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