benjamin dickman

+1

same #2solve, missed the mathier first word !

DTMF 📸

FFTDMFFS

rebumping

The focus on reducing or eliminating "small agencies" can be extraordinarily misguided!

We had an incredible Office of Technology Assessment (OTA) that was eliminated amid the Gingrich R midterms for Clinton I. Still haven't recovered or revived it. Yet!

For more:
en.wikipedia.org/wiki/Office_...

the math edu Mad 🆚 Easy dichotomy... chime in!

#iTeachMath ♾️ #MathSky 🧮

PPS: as a teacher, maddest (most irritated) would be radicals and variables. For example:

"Simplify: √(xy²z³w⁴)"

Oftentimes, textbooks would give incorrect answers!

This one would be:
√(xz) * |yz| * w²

... does that even seem simpler?? I'm unconvinced.

Texts too often do e.g. √(x⁶) = x³. False!

PS: for integers a,b with no common prime factors, there are always integers p,q such that ap+bq=1.

The latter pair has no formal name despite being oft-used; same prof called p,q "Pavlovian integers" to *condition* students into considering their use.

For *years* I thought this was a common term!

Easy: Figuring out whether a variety of Calc II sequences converge. Something that the professor, David Armacost (rip), taught to remind us that we only care about the long-term behavior was the acronym FFTDM (First Few Terms Don't Matter). This was certainly his own, original terminology 😆

Just remove the bottom left L and top right 7. Maybe modify the position means they can't be disappeared entirely (?) but they can certainly be moved such that none of those four is part of a square thereafter...

quick Sat #2solve, an indefensible rise

01001101 01000001 01010100 01011010 01001111 01001000 00100000 01001000 01011001 01010000 01001111 01000011 01010010 01001001 01010011 01011001

1990

same Wed #2solve

salvadoreño cansado

(the first word is a term sometimes used for people from El Salvador!)

axiomatic trigonometry for intro to proofs?!
math.stackexchange.com/a/3310782/37...

direct link to the axioms:
drive.google.com/file/d/1rFkK...

(Axiom IV can be simplified slightly as described in the MSE post from me above)

#iTeachMath ♾️ #MathSky 🧮

same Tue solve #2solve

🫸🏻🔥🪲🫷🏻

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good problem!

same tiny #2solve for Monday

Sun #2solve; ululates on the beach

01001000 01001111 01010111 01001100 01010011 00100000 01010011 01010101 01001110 01000010 01000001 01001011 01001001 01001110 01000111

Sat #2solve:
Almost Merlin (...Erlin?) and all that jazz

01001001 01011010 01000001 01010010 01000100 01010011 00100000 01010011 01000001 01011000 01001111 01010000 01001000 01001111 01001110 01001001 01010011 01010100

Big sky with a thin strip of land and some body of water, possibly the Susquehanna River. There are many clouds dispersed discretely but densely.

re:
is this a problem mathematics can fix?

I enjoyed reading the various comments left, too. My view is that the numerics are often being used for a linguistic function (emphasis, juxtaposition, etc) rather than to communicate quantitative truths. And more often than not it's in bad faith!

same but made a = 1/2 to deal w denominators only at the very end!

e.g. this?
bsky.app/profile/benj...

i don't follow how this "trick" was used? i see the final function but what computation was carried out to get there

Ghausst

i(-3+i) = -1 - 3i

x² = 1 shift x to x+3i:
(x+3i)² = 1
x² + 6ix - 10 = 0

change x to ix:
-x² - 6x - 10 = 0

which is the quadratic found earlier, repeatedly (multiplied by -1)

so... the shift can be done by a complex value, too!

using
x² = 9 for x = -3
then changing x to x-i:
x² - 2ix - 10 = 0

gives the right root, but coefficients are not integral

would like to sub ix for x:
-x² + 2x - 10 = 0

but this multiplies roots by -i

SO

instead we can start with desired root multiplied by i, and then use this method.

that is:

same Fri #2solve,

"↘️💋"