Then at each stage the midpoints of these corners and the centre point are displaced by an amount = where is the average value of the adjacent corners, decreases at each stage (say, by a factor of 2) ...

Paul Carter, David Lowry-Duda, On Functions Whose Mean Value Abscissas Are Midpoints, with Connections to Harmonic Functions, The American Mathematical Monthly, Vol. 124, No. 6 (June-July 2017), pp.

I'll let you work out your own proof of this theorem, but I'll give you a hint. Here's a useful fact: in any triangle, if you connect the midpoints of two sides by a line segment, then that ...

It charts the numeric variable AGE, with the frequency statistic. Because the values of AGE are continuous, the procedure automatically divides the ages into ranges and displays the midpoint of each ...