ℝolliℵg M∀th Thr∑a∂

“Most parents.” *sigh*

Looking forward to another semester of calculus review I mean helping the one kid with her homework. Her minute older sister never seems to request any assistance, at least of that nature.

I believe that search term idea originated with ilxor j., as I can confirm by searching the term.

Actually, speaking as one of the apparently few parents who can actually solve that problem, I do remember sometimes having some kind of anxiety about which way to chop up the figure so I would be least likely to make a mistake in the calculations and could hopefully do it all in my head.

In this case I subtracted earlier rather than later.

> starting a fight on the ilx maths thread by insisting that subtraction is more complicated than multiplication :)

this exactly!

having seen their answer i decided to do area of big block - area of the missing top right block. easy to confirm by testing it with a couple of values for x.

i don't think it's surprising or even particularly concerning that most parents can't do a GCSE maths question

mainstream secondary school math curricula are all horrible, just Cold War artifacts unsuited to either the exploration of math as a liberal art or to its practical applications in basically any career.

at least such was my experience in the aughts and I have no reason to believe anything has changed all that much

what's interesting is that people who are interested in "secondary math as gatekeeper for physical science education" and people who are interested in "secondary math as a liberal art" and people who are interested in "practical career applications of secondary math" and people who are interested in "abolish compulsory secondary math education" all agree with you, but each for different reasons

as long as they all line up behind my reform program I don't care what motivations they have

This is a fun one:

https://mindyourdecisions.com/blog/wp-content/uploads/2018/09/homework-in-china-how-tall-table-preview-600.png

No multiplication required.

table is 150, will show working on request but i couldn't remember what happens if you try to hide several paragraphs on ilx

also i found a less round-the-wrekin way to do it

B-b-but did you also calculate how much taller the cat is than the turtle?

anywhere between 1.15x and infinitely...

yes i know that too

tab + tur - cat = 130, tab - tur + cat = 170, just add them together to get tab + tab = 300

hence cat - tur = 20, however i do not believe we can calculate cat or tur in themselves despite knowing the diff between them

i assumed tur=0 to (marginally) simplify things

MIND YOUR DECISIONS ILXOR LEDGE

but both the creature heights disappear when you add the two, no need to assume anything!

i know. nevertheless, i like assuming.

I used the sin double angle formula.

No I didn’t but it is vaguely related

i do not believe we can calculate cat or tur in themselves despite knowing the diff between them

― mark s

yes, more unknowns than equations

even more unknowns: how many kids (out of all the kids in china) are doing this problem, how many do it correctly, do they do it with help, are they expected to get it right, why do we even care

Here's a question for y'all: what are the maximum heights of the cat and the turtle?

also, how is that table still standing with that cat sat on the edge like it is?

table is bolted to the floor, next question

maximum height of the cat is the height of the table, no? what's interesting is that as you make one animal taller, the other gets taller with it. that seem counterintuitive to me but that intuition is probably just based on my accumulated experience of (superficially) similar problems

the picture breaks if the cat gets bigger than the table but I'm not sure the maths does.

Right. Turtle will eventually break the table too.

have only just noticed that this is the average of the two values. is that always true?

yeah, trivial

yes bcz of yr post at 16.22 london time

https://www.youtube.com/watch?v=tS8oyl1gygs

Slight variation on the problem: instead of limiting ourselves to 2 measurements and 2 animals, imagine we could do a million measurements. For each measurement we select at random two animals from the total animal population of earth. We place one animal on the floor and one on the table (assume table is of infinite strength), and measure the distance between the top of the floor animal to the top of the table animal (which could be a positive or negative number). Given measurements M1 through M1000000, what is our best estimate of the actual height of the table?

51"

Bear in mind that if we select 2 million animals at random from total earth animal population, its likely that most or all will be bacteria and hence of negligible height.

bacteria aren't animals!

You're right. Please disregard my previous statement. It seems the most common animal will be an insect, whose height may or may not introduce significant error in our measurement, depending on the height of the table.

Come now Let us be crooked but never common.

Challenging myself to figure out why this works:

https://pbs.twimg.com/media/FmBgdAxWAAA_O_h?format=jpg&name=small

Happy to explain if you don't figure it out

Oh, I'll let it percolate in the back of my mind for at least a day or two before relenting and looking for hints. Interestingly this trick doesn't preserve the remainder of the number after division by seven in the general case. Only in the case of remainder zero. So its not a perfect modular algorithm.

Took me a few minutes of percolating but it makes perfect sense now.

Thought of two ways to do it. One is more obvious and clear, one is slightly fancier but more interesting. They both amount to the same thing anyway.

Can’t believe I never came across that before. I did spend time long ago thinking about why the decimal representation of one seventh is what it is though.

Not much percolating in my brain yet, except a vague idea that the equation 5 * 10 - 1 = 7 ^ 2 is somehow involved.