Visualizations
An illusion of predictability in scientific results
Even experts think / that well-estimated means / are certain outcomes. (Haiku summary due to MSR poets Dan and Jake). Click the thumbnail for a mini-explainer.
An illusion of predictability in scientific results
Sam Zhang, Patrick R Heck, Michelle Meyer, Christopher F Chabris, Daniel G Goldstein, Jake M Hofman     PNAS, 2023 [paper]
[link] [source]
Elliptic curves and traveling wave solutions to the KdV equations
View traveling wave solutions to the KdV equations associated with (points of) elliptic curves.
[link] [source]
Ridge unfolding polytopes
Unfold 4-dimensional polytopes using their spanning trees.
Visualizing and unfolding nets of 4-polytopes
Satyan L Devadoss, Matthew S Harvey, Sam Zhang     SoCG, 2022 [paper]
[link] [source]
Bayesian inference for COVID-19 testing
My brief foray into epidemiology at the start of COVID-19. Bayesian methods and interactive tools for informing COVID-19 surveillance testing strategies.
Estimating SARS-CoV-2 seroprevalence and epidemiological parameters with uncertainty from serological surveys
Daniel B Larremore, Bailey K Fosdick, Kate M Bubar, Sam Zhang, Stephen M Kissler, C Jessica E Metcalf, Caroline O Buckee, Yonatan H Grad     eLife, 2021 [paper]
Optimizing prevalence estimates for a novel pathogen by reducing uncertainty in test characteristics
Daniel B Larremore, Bailey K Fosdick, Sam Zhang, Yonatan H Grad     Epidemics, 2022 [paper]
[link] [link] [link] [link] [source]
Curve shortening
Deform a curve with a discrete curve shortening flow.
[link] [fullscreen] [source]
A catastrophe machine
Move the center of gravity of a wedge balancing on a table, and observe its corresponding catastrophe surface.
[link] [fullscreen] [source]
Linear regression, the old fashioned way
Perform ordinary least squares through a set of points with nails, springs, sleeves, and a frictionless rod.
[link] [fullscreen] [source]
A moduli space for triangles
A solution to a problem by Lewis Carroll using a clever moduli space. For fun, pick points on the moduli space, and watch triangles deform between them along geodesics.
[link] [fullscreen] [source]
The cross-section of a cylinder is an ellipse
A classical proof that the cross-section of a cylinder is an ellipse. I have no idea why, but this is the most popular blog post on my website.
[link] [fullscreen]
Whitney's Umbrella
First steps in visualizing 3d mathematics using javascript. A famous surface with a cuspidal point.
[link] [fullscreen]
Voronoizer bookmarklet
Draw a Voronoi diagram over any webpage with this bookmarklet.
[link] [source]
Voronoize this page!
This page has a Voronoi diagram drawn over it, with link and input HTML elements as points.
[link] [source]
Treasure hunting
You have been given flawed instructions for finding treasure on an island, but geometry may be able to help.
[link] [source]
An ascii implicit function plotter
Plot an elliptic curve (or any implicit function) using ASCII art!
[link] [source]
Hypocycloids
What happens if you rotate a smaller circle inside of a larger circle?
[link] [source]
Cats on ladders
A cat is sitting on a ladder leaning against the wall, and the ladder slips. What shape does the cat draw through the air?
[link] [source]
A network look at integer sequences
The Online Encyclopedia of Integer Sequences (OEIS) from a 10,000 foot view.
[link]
A visualization of a geometric bound on convex hulls
A lemma that bounds the size of a convex hull of points based off circles centered at those points.
[link] [source]
Building a municipal land use code search engine using a graph of word embeddings
Using the geometry of language to help permit-seekers find the right municipal land use codes.
[link]

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