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• murshid_islam
In summary, the conversation revolves around the validity and precision of Michael's statement in his video about Thales's Theorem. It is pointed out that what he mentions is actually the converse of the theorem, and that it may be argued as incomplete. The conversation also touches on the definition and authority of what constitutes a theorem.
murshid_islam
TL;DR Summary
Is this Thales's Theorem or the converse of Thales's Theorem?
Here is the video in question:

In the video at 4:23, Michael says, "Now Thales's Theorem tells us that the two other points, where these rays contact the circumference, are diametrically opposed. They are on opposite sides of the circle and a line passing through them will pass through the centre."

Isn't that the converse of Thales's Theorem? Yes, the converse is true as well, but what was stated in the video isn't Thales's theorem; it's the converse as far as I understand. Am I missing something?

You are correct - it is the converse and, in this case, the converse is also true.

That said, it is a combination of Thales's Theorem and other logic that would tell us that those two points are diametrically opposed. So his statement "Thales's Theorem tells us that the two other points, where these rays contact the circumference, are diametrically opposed" is arguably correct or arguably incomplete.

Since the title of his Video is "Thales's Theorem", he should probably have been more precise.

It's a relatively trivial consequence of the theorem, or even part of the theorem if you prefer that view. There is no authority that would define what exactly is part of a theorem and what is not.*

*even though I had a professor thinking they would be that authority

## 1. What is Thales's Theorem?

Thales's Theorem is a mathematical theorem named after the ancient Greek mathematician Thales of Miletus. It states that if a triangle is inscribed in a circle, with one side being a diameter of the circle, then the angle opposite to that side is a right angle.

## 2. How is Thales's Theorem used in real life?

Thales's Theorem has various applications in geometry, trigonometry, and engineering. It is used to calculate the height of tall objects, such as buildings and trees, by measuring their shadows. It is also used in navigation and surveying to determine the distance between two points.

## 3. What is the proof of Thales's Theorem?

The proof of Thales's Theorem involves using the properties of inscribed angles and central angles in a circle. It can be proven using basic geometry principles and theorems, such as the Pythagorean Theorem and the Angle Sum Theorem.

## 4. Can Thales's Theorem be generalized to other shapes?

Yes, Thales's Theorem can be generalized to any cyclic quadrilateral, where all four vertices lie on a circle. In this case, the opposite angles are supplementary (add up to 180 degrees) instead of being right angles.

## 5. Are there any real-life examples of Thales's Theorem?

Yes, there are many real-life examples of Thales's Theorem. One common example is the sundial, where the shadow of the gnomon (the stick that casts the shadow) follows a circular path and the angle between the gnomon and the ground is always a right angle at noon.

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