Zingel

New Website

Sun, 10 Nov 2024 09:50:26 +1100

Today marks the release of my newly created website!

This was a fun project to make and only took me a weekend or so to complete. The static site is compiled with Hugo and embeds KaTex in each page to render the math.

Shoutout to ChatGPT for helping with the CSS styles!

Circumference of an Ellipse

Mon, 04 Nov 2024 21:44:31 +1100

I saw this meme recently floating around the web.

Surely it can’t be that hard to find the circumference of an ellipse? For axes of $a$ and $b$ wouldn’t it simply be something like $P=2\pi (a+b)/2$ in a similar way to a circle being $P=2\pi r$?

We can derive the formula ourselves to check this.

First we calculate the length of a small arc around the ellipse $dl$ and then sum them all together as we vary the angle and integrate $\theta$ from 0 to $2\pi$. For a very small length we can use Pythagoras and express the displacement in terms of $dx$ and $dy$.

Lonpos Puzzle Solver

Mon, 19 Dec 2022 09:21:31 +1300

I have a little puzzle that has sat on my desk for years. While I’ve never spent the time necessary to solve it myself, something about the simplicity of it made me never throw it away.

The fact that I’d never solved it before bugged me though, and so with one weekend free I decided to finally solve the puzzle… completely. According to the outside of the box the puzzle has $21,200$ solutions, so I attempted to find them all.

High school Physics Formula Derivation

Tue, 13 Dec 2022 14:46:42 +1300

High School Physics Formula Derivation

It is common practice to get formula sheets for physics exams. Doing physics isn’t just about memorization and so these sheets remind you of the equations, but they don’t give any explanations for how they work. Yet the problem of doing physics this way is that it can lead to an axiomal fallacy.

An axiom is something that we assume to be true. The idea is that you choose as few axioms as possible and then use them as foundations to build upon. A famous example is Euclid’s five axioms from which it is possible to derive all of planar geometry. These five rules, which we cannot test and so assume to be true, contain within them all the information needed to understand geometry. It is simply up to us to reshape them into a form that makes it easier to understand.

Using Machine Learning to find Ambiguous Handwritten Digits

Mon, 04 Oct 2021 09:21:31 +1300

Using Machine Learning to find Ambiguous Handwritten Digits

Note that this post was written two years before ChatGPT, GPT-4 and all its friends were released. Thus, the method used here are already out of date! The principals remain the same, however.

We used to think that computers could only answer math problems, but they have come a long way since then. Computers have moved beyond just understanding text to also understanding images.