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Mind Your Decisions - maths fail

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Watch the first minute or so of his recent video, until he’s explained the question, then press pause:

He rambles on for another five minutes explaining, rather too quickly, an unnecessarily complicated way of working it out. Try doing it my way (below) first to really torture yourself when you aer watching it!

I left the following comment:

Far too complicated!

It’s length 4 from one corner of a hexagon to the opposite corner.
‘Vertical’ height of each triangle in the hexagon = sq rt 3.
Put the square flat on the table, fold up the flaps and look at it from the side.
Point E/F is 1 ‘across’ and has hypotenuse sq rt 3.
Acos 1/sq rt 3 = 54.74 deg (no need to know length of the other side).

Then rotate the square so that you are looking at it diagonally from one corner.
Distance from E/F to a point diagonally opposite (assuming there are four hexagons all folded up) = 4 x sq rt 2.
Distance diagonally across the square = 2 x sq rt 2.
So point E/F is sq rt 2 ‘across’ and has hypotenuse 2 (side length of hexagon).
Acos sq rt 2/2 = 45 deg (no need to know length of the other side).

Took my daugher two minutes once I had explained the basic approach. OK, she’s studying maths…



Source: http://markwadsworth.blogspot.com/2022/08/mind-your-decisions-maths-fail.html


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