lecture 23: sharp projection theorems, part 2: ad regular case
Aaron Pham
up: mit 18.156 Orponen and Shmerkin proved a sharp projection theorem for sets with self-similar spacing. metadata type: video youtube: I6ZSrgxiofs source: mit opencourseware
math
Mathematical Notation to Python Mapping
eloycoto
I did not attend college, so I learned a lot of things on my own. I'm good at Math, but because I learned math using programming languages, the Math language is always something I need to read ten times to understand. This is a map model for me. Nowadays I'm reading a lot of math papers, and I...
Updated “MaC Fund”: The MathAndCobb Fund for Mathematical Exploration
Álvaro Lozano-Robledo
I have decided to upgrade the scope of the MathAndCobb Fund. You can have a look here at the previous announcement. As I explained in my previous post, my content generates “content creator funds” and I decided to give back to the math community, and create my own mini-grant. The MaC Fund was,...
Measuring Confidence
Blog
*, *::before, *::after { box-sizing: border-box; } img { box-shadow: 5px 5px 5px grey; border: 1px solid grey; display: block; margin: 30px auto 30px; max-width: calc(100% - 60px); } At the start of each year, Ron Minsky (from Jane Street) runs a...
Subtracting times
Blog
*, *::before, *::after { box-sizing: border-box; } img { box-shadow: 5px 5px 5px grey; border: 1px solid grey; display: block; margin: 30px auto 30px; max-width: calc(100% - 60px); } In my 7 year old’s math class, they’re learning about time. In...
Animation I’ve done for explaining part of my research.
1ucasvb's lab
Animation I’ve done for explaining part of my research.
Extending tetration to rational heights (a failed attempt)
Blog
*, *::before, *::after { box-sizing: border-box; } img { box-shadow: 5px 5px 5px grey; border: 1px solid grey; display: block; margin: 30px auto 30px; max-width: calc(100% - 60px); } .info { display:flex; align-items:center; border-radius: 5px; } This post is...
Let’s build an operator
Blog
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Guess the function
Blog
img { box-shadow: 5px 5px 5px grey; border: 1px solid grey; display: block; margin: 30px auto 30px; max-width: 100%; } Let’s play a game. I’m going to draw two points on an x-y plane and give you a rule which you can use to generate new points. You can generate as many new points as you...
Tupper's self-referential formula
Atul Vinayak
I saw this old tweet today Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane. pic.twitter.com/R0L3ZjqcyP— Fermat's Library (@fermatslibrary) December 13, 2021 The equation here is not the full picture. The...
Two Percolation Puzzles
Adam Scherlis
Take a very large chessboard (NxN, where N is huge). Remove some fraction 1-p of the squares at random, leaving a fraction p of them. Can you place a queen on the first row and then, via some sequence of legal moves, get it to the last row? This is probabilistic, of course, but it turns...
A hundredth of a bit of extra entropy
Adam Scherlis
There are two ways to calculate the amount of information in one term of a continued fraction: The entropy of the Gauss-Kuzmin distribution is about 3.4325 bits. Twice the logarithm of the Khinchin-Lévy constant is about 3.4237 bits. These differ by about 0.0088 bits. It took me a while...
Math, Art, Tessellations: an Interview with Robert Fathauer
Maria Mannone
Robert Fathauer. http://saxonartgallery.com/hu/muveszek/robert-fathauer/ Mathematicians, to prove their theorems, write on blackboards, paper, and parchment; as history tells us, even sand, like Archimedes. One uses clay. Here we present the work of Robert Fathauer, a...
Photo
1ucasvb's lab
Photo
1ucasvb's lab
Probability and Types
Lawrence Pan
Introduction In this blog post, I will explain the concept of a Random Variable from a software developer’s perspective. Definitions Before we dive in, I want to define a few terminologies, for those of you who are new to probability and statistics. Feel free to skip this section if you think...
One of the best TV shows about physics is now on YouTube!
1ucasvb's lab
Caltech recently announced the release on YouTube of the excellent educational TV show The Mechanical Universe, which gives an accessible but still formal approach to physics and physics history. The show pioneered the use of technical 3D animations as a way to explain complex math and physics...
Vote on which topic you want to see covered next!
1ucasvb's lab
I’m planning a few posts in the near future, but I’m wondering which topic interests people more. The topics I’m considering: Mirrors of different shapes: I’ll explore how rays and waves are reflected by different shapes, and some interesting properties of these shapes. I have more ideas beyond...
Can you flatten a sphere? The answer is NO, you can not. This...
1ucasvb's lab
Can you flatten a sphere? The answer is NO, you can not. This is why all map projections are innacurate and distorted, requiring some form of compromise between how accurate the angles, distances and areas in a globe are represented. This is all due to Gauss’s Theorema Egregium, which dictates...
Figured I’d add a mass in there. See also: previous GIF.
1ucasvb's lab
Figured I’d add a mass in there. See also: previous GIF.
What are your thoughts on the pi v. tau debate?
1ucasvb's lab
(For those unaware of the Pi. vs. Tau debate, read the Tau Manifesto and then the Pi Manifesto).I'm actually extremely pro-tau, but only under certain conditions. I'll explain.Warning: The following is my personal take on these subjects. I'm no authority. This is pretty much late night armchair...
Matrix Sketching
Jeffrey Wang
Last time, I wrote about a clever algorithm for approximating the histogram for a stream using bounded memory. The post was motivated by this paper, which is an extension of that algorithm to a problem that seems unrelated at first glance, which is matrix sketching. The matrix sketching problem is...
Streaming Frequency Approximation
Jeffrey Wang
It's been a while, but I finally motivated myself to write another blog post! Today's topic is approximating the frequency of items in a stream. With all the data that is generated today, streaming algorithms have become very popular as one of the efficient ways to process datasets that are far...