Extra Polynymous
Archimedes found good estimates of pi by computing the perimeter of regular polygons that fit snugly inside and outside a circle. I’d like to take this basic approach and add some more modern twists. I say more modern, but I don’t mean cutting-edge. Taylor series are from the 1700s CE, compared to Archimedes living in […]
What does a minimum force airfoil look like? I basically want to make a fairing that minimizes the total force over the range of 0-5 degrees. This mostly means reducing the lift generated at non-zero angles of attack, while keeping the drag manageable. Minimizing lift on an airfoil feels oddly perverse. I suppose that’s why […]
The four-digit NACA airfoil is perfectly decent, which is a bit surprising considering it was first published way back in 1933. Since it was designed before computers, I’m sure that it could be improved. The general form of the thickness equation is: This does not provide the proper thickness, but ensures a rounded leading edge […]
Airfoils are generally thickest somewhere around the middle. The classic NACA four-digit airfoils are thickest at 30% of the chord, and laminar flow airfoils are thicker around the 50% mark. Let’s throw out the received wisdom and make some airfoils that are thickest close to the front. Rather than working with a lifting body, let’s […]
I wanted to know what a point vortex would do near a corner with an arbitrary angle. Time to dust off the complex analysis! A really useful summary of using complex analysis to model potential flow is here. I will use the method of images to ensure that there is no flow through the wall, […]
I want to have the ink on a photo clump together, leading to a black and white image. This is a sort of flow, so my first thought is to take a look at the advection-diffusion equation. Let’s say that the ink distribution across an image is , the diffusion factor is , and the […]
Previously, I took one photo and rearranged its squares to make a version of another photo. How about a sillier version, where you use one image to re-make itself? The simple answer is to just keep every square in its original place, but that’s no fun at all. Instead, we can add the requirement that […]
In my previous post, I did some statistical analyses of the Dresden Files novels. Now I want to do some fancy stuff with vectors. Word2Vec is a method for turning a bunch of words in text into related vectors, as the name implies. Using a shallow neural network, it represents finds vectors such that words […]
The Dresden Files is a series of very fun books by Jim Butcher, with a wizard detective getting into trouble and saving the world and all that. I’ve wanted do do some Natural Language Processing (NLP) on a body of text, and with fifteen novels so far (two more later this year!), this is a […]
Previously, I recreated an image by rearranging squares of another image. Typical photomosaics allow for repeated use of tiles, so I’ll try that for comparison. I’ll still allow rotation, as it helps the edges so much. The image on the left is the result: It works, but isn’t great. The repeated use of certain tiles […]