Activity 3: One of the Baudhayana Sulbasutras
One of the Baudhayana Sulbasutras says
If it is desired to transform a rectangle into a square, its breadth is taken as the side of a square [and this square on the breadth is cut off from the rectangle]. The remainder [of the rectangle] is divided into two equal parts and placed on two sides [one part on each]. The empty space [in the corner] is filled up with a [square] piece. The removal of it [of the square piece from the square thus formed to get the required square] has been stated [before],
In the app, the larger (blue) square has side length a, and the smaller (pink) square has side length b. Now, you can do this constructions in the app or on paper.
- Choose a vertex V of the larger square, and a side s emanating from V.
- Mark the point A on the side s at distance b of the vertex V (Hint: Use the compass). Recall b is the length side of the smaller square, so you are "copying" the side of the smaller square in the large square.
- Erect a perpendicular to s passing through A. This perpendicular intersects the side opposite to s on a point B.
- Draw a circle with center A and passing through B.
- Denote by C the intersection of this circle with the side of the square emanating from V.
- Construct a square with side AC
- Answer the question in PollsEverywhere. (Activity 3: Why the area of the square you constructed is the difference of the areas of the given squares).