Today we explored one of the most famous recursive sequences called The Logistic Map.
Try this activity leading on to exploring the sequence on Geogebra. There are Geogebra instructions here if you get stuck.
We were inspired for this activity by this amazing video from Ben Sparks on Numberphile. It explains how this activity links to one of the Feigenbaum constants, pseudo ramdom numbers and Chaos Theory. Definitely worth watching!
The first question of today is how many sides a piece of paper has. So the answer is 2 of course. Now we want to find a way of folding the paper in such a way that there is only one side. One way to verify this is to take a pen and colour the folded piece of paper. If you do not need to turn the piece of paper around, there is only one side. The method to do this is to twist the piece of paper by half a turn and you will obtain a möbius band.
This is all explained in this presentation from Suffolk maths, that also contains a brilliant exploration table. Your challenge is to fill in the first three lines and to come up with three other results to add to the table below.
Good luck!
This week we worked through another brilliant puzzle from the Math Pickle team called McGuire the Gathering.
Lots of fun trying to solve both on pen and paper and with excel!