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?
(compared to python when it is forced to apply arbitrary functions with loops inside, element-wise to an array - that is, can't benefit from vectorised numpy functions)
this #maths experiment took about an hour in python and about 1 second in julia lang
sure my python isn't professional, but today was my first time with julia lang so that will be far from optimal either
"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
I bet that a lot of people in the Fediverse already know this very pretty pencil-based 3D art. But in case you haven’t, be prepared to marvel.
This sculpture is known as the hexastix and a variant series created by artist George Hart is titled 72 Pencils.
If you can get 72 unsharpened hexagonal pencils, and some flat rubber bands, you can attempt to create this. Search for a video by @standupmaths for a pseudo-tutorial.
"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
Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic#curve with #period over the #circle's circumference and has #cusps whenever the point is in contact with the surface (the two sides of the curve are tangentially vertical at that point).
Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.
A five-star rating for Everything is Predictable: How Bayes' Remarkable Theorem Explains the World by Tom Chivers, from Brian Clegg at Popular Science Books.
Question for #maths folks. Are there any "proofs for kids" type resources out there? Like suitable for a 10 year old.
Just over dinner watched eldest work through what day of the week youngest's birthday will fall on in various years.
(I've no idea if they were getting it right, but...)
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." – Bertrand Russell (1872–1970) #quote#mathematics#maths#math
Just started writing up a few of my notes on introductory Category Theory. Not much here yet (it took me awhile to get Figure 1 to look right, and it's still not perfect).
One of my personal objectives for learning #maths is to understand the connection between the zeros of the Riemann Zeta function and the distribution of primes.
That's not an open question - it is known. But not by me.
I want to understand it in more detail than the hand-wavy explanations in popular science books. ... I have a lot of foundational learning to do before I get there.
A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings?
e.g. for a target of 19 a candidate representative would be 1011213141516171819 in base 10, that has 19 digits. Can it be done in less, or is $\sigma_10(19) = 19$?
Can we find a general rule? Any properties of this function?
Today, 200 students from schools in Tirol, Vorarlberg and Salzburg are taking part in the international #Mathematics Competition #Naboj at the University of Innsbruck #study#maths