cas

they had the vocabulary of a 2 year old and rocky was already flaming grace :')

The familiar, hierarchical sequence of math instruction starts with counting, followed by addition and subtraction, then multiplication and division. The computational set expands to include bigger and bigger numbers, and at some point, fractions enter the picture, too. Then in early adolescence, students are introduced to patterns of numbers and letters, in the entirely new subject of algebra. A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math.

But this progression actually “has nothing to do with how people think, how children grow and learn, or how mathematics is built,” says pioneering math educator and curriculum designer Maria Droujkova. She echoes a number of voices from around the world that want to revolutionize the way math is taught, bringing it more in line with these principles.

The current sequence is merely an entrenched historical accident that strips much of the fun out of what she describes as the “playful universe” of mathematics, with its more than 60 top-level disciplines, and its manifestations in everything from weaving to building, nature, music and art. Worse, the standard curriculum starts with arithmetic, which Droujkova says is much harder for young children than playful activities based on supposedly more advanced fields of mathematics.

yeah. and you can even include "thing that reduces the barrier to doing the task" as a catalyst/enzyme

warning: blood, and Grace frying the ever-loving heck out of his arm

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

-> 24 + 13 + 2 = 39 feet

original post

bonus: