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 x3+y3+z3 = 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).
If you place squares on the sides of any parallelogram, their centers will always form a square.
A visual intuitive proof that √ab cannot be larger than (a+b)/2, where a, b ∈ R*+