God forbid we ever have to weigh options and make the smallest goddamn decisions in our own lives

My first guess is an elliptical arc, if we assume that the swing itself is swinging in a circular arc, and the rays from the sun are basically parallel

Yeah pretty much anything U-shaped is a parabola.

The graph of y = sec x? Bunch o' parabolas.

A parabola rolls along a flat surface.

What path does its focus (the red point) trace? Another parabola? Or something else?
#iTeachMath #math #maths #mathgif #mathgifs #mathsgif #mathsgifs

Only very briefly. Today I introduced the idea of “logarithms” in U_n, and suggested it might help identify which elements were “perfect squares,” and we were off to the races

Today in Advanced Topics we tried to create a "quadratic formula" for solving quadratic equations in ℤₙ.

I'd never done that before. Wasn't planning on doing it today. But that's where our rabbit hole led us.

We haven't worked out all the kinks, but the messiness is part of the fun. (Ask any kid.)

An xy projection of the 3D Halverson attractor.

I coded it in #Mathematica, then asked #ChatGPT to port it to html/js so it can run in a browser. That's what you're seeing here.

Let $S_n$ denote the sum of the first $n$ terms of a particular arithmetic sequence. If $S_{50}=200$ and $S_{200}=50$, for what value of $n$ does $S_n$ attain its maximum value?

Springtime in Algebra II Honors is fun-arithmetic-sequence-problems season...
#iTeachMath #iTeachMaths #math #maths

For extra credit, use only the four arithmetic operations (integer exponents count) and the absolute value function

Four unit spheres, centered at (±1,±1,0)... and their convex hull.
Each in a single line in #Desmos 3D.
Can you do it?
#iTeachMath #math #maths #geometry
desmos.com/3d

> image of Jesus eating a hotdog, the text underneath it reading “He Is Glizzin’”

NO FLOWS CREATED Ready to create your first flow?

What fresh hell is this

Interesting. Never heard of it! Where did you learn it?

My 15yo son manages to get pizza sauce on every new article of clothing the first time he wears it.

Even if we haven't eaten pizza. Somehow he still makes it happen.

Huh. I'm not seeing it. Say more!

Suppose $x=\log_2{30}$ and $y=\log_2{5}$. Which of the following can be written in terms of x and y? How? (Be prepared to explain your answers.) $\log_2{6}$ $\log_2{10}$ $\log_2{15}$ $\log_2{20}$ $\log_2{25}$ $\log_2{35}$ $\log_2{125}$ $\log_2{150}$

Going to try to discover some log rules in Alg II Honors today
#iTeachMath

A jar of Biscoff Creamy Cookie Butter

My kids introduced me to this and I will never forgive them for it

Two blocks of extra-firm tofu, between two cloths, with a metal case full of poker chips

Kitchen hack: Use a poker chip set—heavy, but low center of gravity—to press tofu

A "making of" my #mathart post from yesterday

#mathart

🙄

Just checking in on my Janus account. This is what I see (minus personal specifics): the Contrarian fund living up to its name

Ha yeah I don't have that. This took me... a long time to arrive at.

One minute you're puzzling over a simple probability question, the next minute you're unironically typing out an expression that looks like this

I may have, years ago. And I made up the problem! Back in 2009 or so.

Hyperbolic surfaces spotted at the Andrew Gn exhibit at the Peabody Essex Museum

🤷🏼‍♂️

But I think that there is an optimal overall strategy.

You pick a coin and flip it. It comes up Heads. What should you do next? Flip the same one again, or flip a different one?

This is just one of the many questions that arise...

I've seen some people say, for example, that if the first flip yields Heads, then for Flip #2 you should flip that same coin a second time, otherwise flip a different coin. 🤷‍♂️