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I've recently started to create geometric drawings (axonometry) of mathematical functions, the same ones I usually tackle with code.

One could say it does not make sense to painstakingly draw what code could create quickly. But for me the interesting thing is to grasp these functions on a different, more intuitive level - compared to mentally processing mathematical formulae or casting it into computer code. After literally decades of dealing with mathematical expressions and code I have rediscovered descriptive geometry, as sort of a "third language" (in addition to math or code) to say the same things. I am also fascinated by the little math puzzles that pop up when I create these drawings, and which require a completely different approach than calculations or programming.

I am usually drawing them at least three times, until I am somewhat satisfied. The journey is the reward anyway :-)

Here is the work-in-progress photo of my taming two favorite functions of mine - often already used in my creative coding art. I called them "Reality and Imagination" as these are two "towers" or "trumpets" that represent real and imaginary part of the complex function 1/z. Grand words, but you also describe them as: Stack circular rings upon each, ring diameter decreasing reciprocally with height, align along the circumference. Then flip over, and then rotate by 90 degrees.

Circles are just ellipses, seems to be easy, but the 2D projections overlap greatly with the 3D axonometric image as I am currently using "small" A4 watercolor paper. The real challenge will be to convey the spirit of this trumpet-like surface without of course create all the giant circles.... as moving closer to the origin of the vertical axis, the radii of the circles get larger and larger, and finally the straight axis is the "circle with infinite radius".

Anyway, I actually do not really want to "explain math", I am more meditating upon these structures :-) I am drawing two versions in parallel - with slightly differently positioned 2D projections, and different sizes of the circles. The version were I colored the ellipses / circles already was the first, more rough one - and I guess I will test something more bold with that one. The other one will maybe become a more delicate drawing. I also admit, that I take a look at the code-generated structures - not for comparing details, but to get the overall look right :-)

#😮 it's beautiful #mathblr #mathematics #technical drawings #descriptive geometry #axonometric

mansand

do i know you...?

nonexistent-creature

I love when a textbook has a theorem that is just the most obviously true shit, like girl I sure hope so, if that weren't true I think math would fall apart!

eiimblr

machine-unlearning

I especially love the conjunction of "this problem is intuitively plain as day" and "it took mathematicians centuries to formally prove this." What do you mean it takes advanced topology to prove every closed curve has an inside and outside

ericvilas

Just in case people weren't sure, it's because these kinds of things are easy to prove in "nice environments", which require tons of assumptions such as "you're not drawing these curves inside a weird bizarre fractal world where geometry doesn't work the way you think", but mathematicians want to prove stuff more generally. What if your sheet of paper has infinite holes in it and your curve weaves through them? What if your curve is defined in a fractally way such that its second derivative doesn't exist at any point but its first derivative does? Etc etc.

The reason physicists get flak from mathematicians for being too nonchalant with proofs is because we tend to assume smoothness and well-behaved functions, which mathematicians can't afford the luxury to do.

callmebliss

Y’ever read something and have understanding that has eluded you interminably suddenly stop, curl up, and snuggle neatly into a fold in your brain because a new way way opened to it?

macleod

I've seen this passed around a few times, and I have one thing to say:

It's online. The book was carefully and wonderfully recreated online by hand. You can find it here. The entire book is this easy.

calculusmadeeasy.org

infiniterectangles

This Valentine's Day, remember: I love u (substitution)

just-shower-thoughts

“X” is probably used more in Mathematics than English

theartofangirling

some memes I made to express my current frustrations with academia feel free to add your own

meme-spren

don’t forget when the motherfuckers write a book and use its easy understandability as a selling point and still do this

studentlifeproblems

@studentlifeproblems

justajournalblog

Calculus. Everything is Calculus and nothing hurts.

A mathematician went insane and believed that he was the differentiation operator. His friends had him placed in a mental hospital until he got better. All day he would go around frightening the other patients by staring at them and saying “I differentiate you!”

One day he met a new patient; and true to form he stared at him and said “I differentiate you!”, but for once, his victim’s expression didn’t change.

Surprised, the mathematician marshalled his energies, stared fiercely at the new patient and said loudly “I differentiate you!”, but still the other man had no reaction. Finally, in frustration, the mathematician screamed out “I DIFFERENTIATE YOU!”

The new patient calmly looked up and said, “You can differentiate me all you like: I’m e to the x.”

I’m sorry, I needed some Calculus to clear my head of all this Chemistry.

Please excuse my interruption in your daily feeds. I’m sorry that I haven’t explained the joke.

redacted-metallum

Optimus ‘

justajournalblog

Warning: Math Joke ahead.

Sorry, I found a really funny (at least to me) math joke. You can judge all you want, but I’ll still love Calculus.

There’s a big calculus party, and all the functions are invited. ln(x) is talking to some trig functions, when he sees his friend e^x sulking in a corner.

ln(x): “What’s wrong ex?” e^x: “I’m so lonely!" ln(x): "Well, you should go integrate yourself into the crowd!" e^x looks up and cries, "It won’t make a difference!”