Pythagoras’ Theorem, Coordinates, and Social Distancing

Pythagoras is undoubtedly one of the most famous philosopher/mathematician. Pythagoras is infamous for the eponymous Pythagorean Theorem. In fact, anthropologists have found that the theorem was found before by other cultures - Babylonians, Egyptians, and the Indians.

The theorem states that the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

Mathematically, the theorem can be expressed as:

If we conflated both the Pythagoras’s theorem and coordinates, we could find the distance between two points.

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The distance AB = 3 which is the difference between the x-values of A and B.

Similarly, BC = 4 which is the difference between the y-values of B and C.

What would happen if the coordinates did not have value, but rather were written in terms of x and y?

Would you be available to find the distance of the hypotenuse?

Let’s explore:

If the coordinates of point A were changed to (x1, y1) and point B to (x2, y2), then the distance of AC would be as follows:

We know that triangle ABC is a right-angled triangle, hence, the Pythagorean theorem should apply.

 

A few weeks ago during lunch, I saw a student X approach student Y’s table. Student X sitting at the table asked Student Y to maintain social distance for safety from Covid, as per New York State regulations.

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As per New York State regulations, the recommended social distance, d, from other individuals is 6’. What geometrical shape (circle, triangle, square, or rectangle) will ensure a 6’ distance? 

Hint: Draw a circle with radius 6. Draw a square/ triangle with sides 6’ to ensure that all the sides are 6’ apart.