Square-a-lune Puzzle of Hippocrates

Source of Inspiration and Reference

Reconstruction GeoGebra Demo

Squaring a Lune Puzzle of Hippocrates https://drive.google.com/file/d/1whLUjEIXiiA9XfULET0x7xK_Q6xqcJ8N/view?usp=sharing

Steps for the Reconstruction

https://bit.ly/4hkrT0M Note: This serves as an application of the integration process for finding the area bounded between two functions. Hence, this puzzle served as an early exposure to the concepts of the integration process.

Ratio of the Each Circle to the Squares of Radii

Please compute the area of each circle and divide it by the square of its radius. What value for the component of the circle did Hippocrates demonstrate?

Select all that apply

A
a) π/2
B
b) π
C
c) d
D
d) 3

Check my answer (3)

Comparing the ratio of the area of circle and the square of radii

What discovery did Hippocrates demonstrated when comparing the ratio of the area of circle and the square of radii?

Select all that apply

A
a) The ratio is proportional to the radius.
B
b) The ratio is the same.
C
c) The ratio is inversely proportional to the radius.
D
d) The ratio is a whole number.

Check my answer (3)

Textbook Reference and Source of Inspiration:

Bondoc, J. M. F., Villa, J. C. S., & Pawilen, G. T. (Eds.). (Year). History of mathematics. Rex Marketing Publisher.