Gravitational Collapse of a Spherical Shell?

A while ago at high school, I was once walking down the hallway when I noticed my beloved physics teacher heading towards me wearing a big smile on his face. I knew what was coming, another one of his classic “try to solve this problem, if you can” moments. However, the level of his excitement […]

July Roundup

Hi, sorry! I know I’ve been quite patchy with these articles and they’re being churned out more like once every two months instead of monthly like I initially intended. I also know this July one is (very) late. I don’t really have an excuse so please just accept my apology. Also, as you can see […]

Machine Learning: k-means clustering

k-means is a popular unsupervised machine learning algorithm for finding clusters in data. In this article we will be learning the intuition behind the k-means algorithm and coding a basic implementation of it. Unfortunately I won’t be delving into the mathematics behind the algorithm (or else the article would be too long!) but there are […]

May Roundup (Maths, Tech, Computing)

Hi everyone! Due to revision and exams, I was unable to complete the April roundup, but I am now back with 3 new stories in the areas of tech/computer science (or really just science in general because let’s be honest, half of the topics that I write about don’t fall under the tech/computer science/maths umbrella). […]

March Roundup (Maths, Tech, Computing)

Can you believe we’re already a quarter of the way through 2018?! March had two significant events, the first being the Cambridge Analytica data breach scandal and the second being the death of Professor Stephen Hawking. I’ll admit the latter is less of a maths, tech or computing story, but I thought his passing was […]

Russell’s Paradox – A wake up call for set theory

Before the philosopher Bertrand Russell began really thinking about the nature of sets, sets were defined informally. Set theory before various axiomatic definitions is now referred to as naïve set theory. Russell’s paradox, discovered by Bertrand Russell in 1901 was also discovered a year earlier by Ernst Zermelo but never published. This paradox shows that […]

Proof of the determinant of a product of square matrices using Leibniz’s equation

Let us consider the square, dimensional matix. It is possible to re-express the matrix in terms of a vector containing its rows. Where It is then possible to express the product of the matrix , with another dimensional square matrix as the following, by the definition of matrix multiplication. Each row of the matrix can […]

February Roundup (Maths, Tech, Computing)

Hi everyone, I’m back with a couple of short summaries on topics that I’ve found significant and/or important in February. As before, links to articles that I used on each of the topics will be included at the bottom of the article in case you want to read more into the subjects. Telugu Symbol Crashes […]

January Roundup (Maths, Tech, Computing)

Welcome to Plancktime’s first ever monthly roundup featuring short summaries on a couple of maths, tech or computing news that I thought were interesting and/or important. Links to articles that I used on each of the topics will be included at the bottom of the article in case you want to read more into the […]

An Introduction to Calculus of Variations

What is Calculus of Variations? In general, developments in mathematics are motivated by the need for them in applications. Calculus of variations is no exception. In fact, it was first developed in 1969 when Johann Bernoulli asked the greatest mathematical minds of his time to solve the famous ‘brachistochrone problem’. This problem involves a bead […]