In 1937, mathematician Victor Thébault found that squares constructed on a parallelogram’s sides yield a square when their centers are connected.

Read more: https://en.wikipedia.org/wiki/Th%C3%A9bault’s_theorem

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# Category: Theorem

## Thébault’s Theorem

## Brahmagupta’s Theorem

## Toeplitz’ Conjecture

## Isogonic Center

## Life, the Universe, and Maths

## Wallace-Simson’s Line Theorem

## Inverse Powers of Phi

## Fibonacci Right Triangle

## Original Proof of the Pythagorean Theorem

## Euler’s Line

In 1937, mathematician Victor Thébault found that squares constructed on a parallelogram’s sides yield a square when their centers are connected.

Read more: https://en.wikipedia.org/wiki/Th%C3%A9bault’s_theorem

If a **cyclic quadrilateral **( = with vertices lying on a common circle) has diagonals which are perpendicular, then the perpendicular to a side from the point of intersection of the diagonals will bisect the opposite side (AF = FD).

Does every simple closed curve in the plane contain the vertices of a square?

No one knows, but the answer to this question is positive if the curve is sufficiently regular.

In geometry, the **isogonic center** (aka Fermat–Torricelli point) of a triangle, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible.

For years, mathematicians have worked to demonstrate that *x*^{3}+*y*^{3}+*z*^{3} = *k*, where *k* is defined as the numbers from 1 to 100. This theory is true in all cases except for an unproven exception: 42.

By 2016 and over a million hours of computation later, researchers of the UK’s Advanced Computing Research Center had its solution for 42.

More intriguing number facts **here**.

The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.

Summation of Alternating Inverse Powers of Phi…

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number.

Clever visual proof by Mike Hirschhorn.

“*Euler’s line*” (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red).

Other notable points that lie on the Euler line include the de Longchamps point, the Schiffler point, the Exeter point, and the Gossard perspector.