To begin this experiment, I first purchased two refrigerator-sized Fractiles-7 sets (available at http://fractiles.com/), and then, early on a Sunday, quietly arranged these rhombus-shaped magnets on the refrigerator in our apartment (population: 4, which includes two math teachers and two teenagers), using a very simple pattern.

Here’s a close-up of the center. There are 32 each, of three types of rhombus., in this double-set, for a total of 96 rhombic magnets, all with the same edge length.

The number of possible arrangements of these rhombi is far greater than the population of Earth.

The next step of the experiment is simple. I wait, and see what happens.

It should be noted that there is a limit on how long I *can* wait before my inner mathematical drives compel me to play with these magnets more, myself — but I do not yet know the extent of that limit.

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What are the angles of the 3 rhombuses?

One is obviously the Golden ratio?

What are the other two?

Regards

Ashok

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The red rhombi have angles measuring pi/7 and 6pi/7 radians — two of each per rhombus, of course, while the yellow rhombi’s angles measure 2pi/7 and 5pi/7 radians. For the blue rhombi, the corresponding figures are 3pi/7 and 4pi/7. While this makes it easy to see why this product has a “7” in its name, the presence of the Golden Ratio in any of this has eluded me.

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