Hipocratic moons

Question 1

What does the Theorem of Hippocratic Moons say?

Accepted Answer

The moons have the same shape as the triangle, The area of the moons equals the area of the triangle

Question 2

Which of the following are true about Hippocrates of Chios?

Accepted Answer

He lived in the 5th century BCE, He was a Greek mathematician, He was interested in geometry

Question 3

Why do we use the fraction 1/2 when calculating the area of the Hippocratic Moons?

Accepted Answer

Because the moons are made from semicircles

Question 4

What was the main goal of Hippocrates of Chios?

Accepted Answer

To calculate curved areas, To square the circle

Question 5

Why do we subtract the semicircle on the hypotenuse when creating the moons?

Accepted Answer

Because we want to isolate the moon-shaped regions, To calculate the leftover curved parts

Question 6

Which of the following were used to create the Hippocratic Moons?

Accepted Answer

Semicircles on the legs, A right triangle, A semicircle on the hypotenuse

Question 7

What mathematical theorem is used in the proof of the Hippocratic Moons?

Accepted Answer

Pythagorean Theorem

Question 8

Who discovered the Hippocratic Moons?

Accepted Answer

Hippocrates of Chios

Question 9

What is the formula for the area of a full circle?

Accepted Answer

πr2

Question 10

What shape are the Hippocratic Moons made from?

Accepted Answer

Semicircles and crescent shapes

Questions 10