Additional fun fact! You can go back/forward two Fibonnaci numbers to approximate inches to cm! This works since the conversion factor, 2.54, is approximately the golden ratio squared (being within 3% of each other).
For example, we would guess that 89 cm is
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
34 in, which is very close to the correct value of ~35.04 in!
With the same divide and conquer method, we could guess that 100 cm is (89 + 8 + 3 -> 34 + 3 + 1) = 38 inches, and the actual value is ~39.3701 inches, so we were only off by an inch!
But why limit it to the Fibonnaci numbers! You can use other recursive sequences to approximate other conversion ratios!
For example, there exists a sequence called the Tribonnaci numbers which goes
0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, ...
where each number is just the sum of the preceding three (compared to the Fibonnaci sequence summing up the previous two). With this sequence, the ratio of consecutive terms approaches the Tribonnaci constant, which is just the real zero of the equation x³ - x² - x - 1 = 0, which is ~1.8392867552...
Now, converting from feet to meters involves multiplying by 0.3048, but one might notice that 0.3048 is approximately 1.83928 / 6, being off by less than a percent! Therefore, to convert from meters to feet, one can:
Multiply the meters by 6 (tricky to do in your head, but doable with practice)
Think of all of the Tribonnaci numbers (not that many small ones)
Split up the meters into Tribonnaci numbers
For each of the split up numbers, go to the previous Tribonnaci number
Add all of them up, and that's the result in feet!
(For feet to meters, split up the numbers, go to the next Tribonnaci number, add them all up, and then divide by 6)
For example, for 12 meters to feet:
12 * 6 = 72 = 44 + 24 + 4
Sure enough, 12 meters is 39.3701 feet!
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