Question

State Thale’s theorem

Answer 1

- Hint: We first look at Thales and then we look at his works and then what Thale's theorem is and where it is used and what are its properties and some history about it. Thales' theorem is a special case of the inscribed angle theorem. The inscribed angle theorem states that an angle $\theta $ inscribed in a circle is half of the central angle $2\theta $ that subtends the same arc on the circle.

Complete step-by-step solution -

Thales of Miletus was a Greek mathematician, astronomer and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded him as the first philosopher in the Greek tradition, and he is otherwise historically recognized as the first individual in Western civilization known to have entertained and engaged in scientific philosophy.
It was Thales who first conceived the principle of explaining the multitude of phenomena by a small number of hypotheses for all the various manifestations of matter. Thales believed that the Earth floats on water and all things come to be from water.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle $\angle ABC$ is a right angle. Thales' theorem is a special case of the inscribed angle theorem.

Note: Through this question one must understand how great Thales was and how much he had contributed to mathematics and the formula that he used to come up with which was used to serve as an amazing gift for the other mathematician. We can also use the inscribed angle theorem and then show that Thales theorem is a special case of inscribed angle theorem.