Im currently working on trajectory systems and forgot what tan() does and I kinda am embarrassed about that. Also I'm awful at trigonometry apparently. Haven't thought about it in a couple decades!
(1/2) Hands-On Mathematical Optimization with Python 🚀
The Hands-On Mathematical Optimization with Python book by Krzysztof Postek, Alessandro Zocca, Joaquim Gromicho, and Jeffrey Kantor provides the foundation for mathematical optimization. As the name implies, the book is hands-on with Python examples, mainly using Pyomo.
I have a question about the aperiodic spectre tile (or the hat/turtle).
I know that the proof of aperiodicity works by showing that the tiles must fit together in a hierarchical structure that eventually repeats itself at a larger scale. But the larger units aren't literally scaled copies of the spectre. I also know that there is some freedom as to how you draw the edges of the spectre.
Is there a way you can draw the edges that allows you to literally use spectres to cover a larger copy of themselves? If so, is this way of doing it unique?
I said this to a room full of people years ago and it turned out to be controversial, so what the heck I'll post it here:
Science results and math theorems should not be named after people, and we should undertake to rename any that currently are. We should prioritize renaming results or theorems named after white men and other privileged categories of people, with special attention to cases where a privileged person accepted or was assigned credit for work a less-privileged person did.
[ \sum_{n=0}^{\infty} {\frac{n^4}{n!}}=15e ]
This is strange enough to provoke wonder, but simple enough to serve as an entry-point to an interesting generalization.
"Mathematics must subdue the flights of our reason; they are the staff of the blind; no one can take a step without them; and to them and experience is due all that is certain in physics." – Voltaire (1694-1778) #quote#mathematics#math#maths
#kdtree and ball trees seem cool, but require full knowledge of the thing I'm searching for. What if it's 7 dimensional and I only know 4 of the values?
I feel like a "parallel kd tree" with a separate binary index on each dimension would work better here.
Reduce depth. Allow unspecified values. It'd also be a snap to create and search each dim in parallel.
One of the current book bundles at HumbleBundle contains 3 books by John Horvath and Rich Cameron featuring #OpenSCAD for visualization and examples (among 15 in total with various topics on electronics and robots).
True story. When I started working on my song, The New Rage, I knew it was for #fedivision so it's working title was "betrayed by math" because @futzle won last year with a very clever math adjacent song. Only thing that remains are the lines "...when it adds up to nothing. Add it to nothing" #fedivision24#math
"Numbers are free creations of the human mind, they serve as a means of apprehending more easily and more sharply the diversity of things." – Richard Dedekind (1831-1916) #quote#mathematics#math#maths#numbers
Ok, this one is for the discrete #math gurus out there.
Let N = CRC32(X)
Given N, is it possible to efficiently calculate CRC32(concat(X, Y)) where Y is a known sized, but very long, sequence of 0xFF bytes?
Obviously you can just seed the CRC with N and iterate, feeding 0xFF in each cycle, but is there any kind of shortcut you can take if you know the input is always a 1 bit?
Brian Conrad, the Stanford mathematician who has written extensively about the problems with the proposed California Mathematics Framework (CMF), is now the subject of a formal complaint filed with Stanford University by the President of the central section of the California Math Council accusing him of "reckless disregard for academic integrity".
Something I keep coming back to as a teacher and learner is Papert's concept of "Objects to Think With". In some ways, math for me is simply a collection of objects to think with. The guitar, too. Card games. The Rubik's cube. A basketball. And a simple way to be a lifelong learner is to continually seek out new objects to think with.
I have an interactive art piece I sometimes bring with me when I go to festivals called “Math Anxiety Camp.” The project consists of a little math book I wrote, more of a pamphlet, full of funny, weird, and famous math problems that are designed to elicit both laughter and anxiety. Problem number 1 is “Name a number that is 3.” Problem 18 asks you to count backwards from 100 by 7s and state the last positive number you count. This problem is known as “serial sevens,” and even has its own Wikipedia page because it is used by psychologists to elicit anxiety in experimental subjects. When I give problems, I try to rush my subjects, and I make buzzing noises when they get wrong answers. I say things math teacher should never say like “You should have learned this last year.”
Good art elicits emoitions, and I know of no other art piece that is designed to elicit the emotion of math anxiety. As a math teacher, math anxiety is an emotion I deal with regularly. Manifesting it at a festival where this emotion is out of context and the stakes are low gives me a novel way to interact with people around their math anxiety, and I’ve learned a lot from adults about their experiences learning mathematics as children.
Anyone who achieves anxiety from my art project wins an a achievement award, namely a yellow sticker. Interestingly, I’m not able to make everyone anxious with my little book of math problems because a lot of people enjoy math. I still give them a sticker if they want one.