In calculus, a derivative is a rate of change. The derivative of position is velocity (how fast your position changes). The derivative of velocity is acceleration (how fast your velocity changes). People don't talk about the derivative of acceleration very much, but when they do, it's called
jerk. I know, silly, right?
Well, the names just get more whimsical from there! Fill in the blanks:
position → velocity → acceleration → jerk → snap → _______ → pop → ____ → drop
Hint
Even physicists make pop culture references.
For bonus points, come up with your own amusing names for the derivatives after drop!
__,١٣,٨,٥,٣,٢,١,١
What comes next?
Answer in the appropriate character set! You can copy and paste from the text above.
Hint
Solution
The answer is ٢١. What we have here is the Fibonacci numbers written in Eastern Arabic numerals. (Western Arabic numerals are the ones we use in English: 0 1 2 3 4 5 6 7 8 9! If you tilt your head, you'll see a resemblance between the Eastern and Western 1, 2, and 3.)
Now, Arabic reads from right to left, so you might be surprised that 13 is written as ١٣ and not ٣١. An inconsistency? Not really! There's no law of the universe that says numbers should be written with the highest-value digit first. I mentioned Al-Khwarizmi yesterday, whose name gave us "algorithm". Al-Khwarizmi's books taught Europeans to do place-value arithmetic using Arabic numerals. And in case you haven't noticed, long addition, subtraction, and multiplication all work from right to left (starting with the low-value digits). If anyone is being inconsistent, it's us left-to-right writers, who borrowed a right-to-left numeral system and never turned it around!
Eastern Arabic numerals remain in use in a number of languages. The image in the hint was from the Central Kurdish Wikipedia page on Fibonacci.
Apologies if I got anything wrong. I don't actually speak Arabic or any related language, so this is all based on my research of how numeral systems work.
Congratulations to yesterday's solvers Connor, Lucia, Cloe, Jacob C., Maddy, Leo S., Yana, Anna J., Anna K., Inca, Jessica, Charlie, Peter M., Nico, Newton, Magoo, Kate, Mr. Gregg, and Graham. Thanks to everybody who made a guess!
Though he now teaches mathematics, Dr. (né Mr.) Shapiro's first job in a K–12 school was as a lunch monitor in Davis, CA. It was there that he originated the Puzzle of the Day, even rewarding correct answers with tickets in denominations like "15 points" (though without a clear idea of how he'd ultimately redeem these). Dr. Shapiro's favorite puzzle from this pre-professional era was "Tell me the location of the beehive on this campus."
Ten years later, Dr. Shapiro revived Puzzle of the Day at Proof School, writing each day's puzzle on a name tag. After 600 puzzles or so, he was just starting to feel normal about students reading his chest all the time when campus closed and the puzzle, like the rest of our lives, moved online. New puzzles are posted daily on school days.
Want to catch up on old PotDs? There's an archive currently containing puzzles from March to June 2020.