An intuitive explanation for why sample means should be normally distributed.

There have been many excellent articles and videos about the Central Limit Theorem (CLT). But besides formal proofs, I was not able to find a good intuitive explanation for why it is true.

So here goes…

Theorem Statement

The remarkable and “counter-intuitive” thing about the CLT is that the original population distribution does not need to be normal, or even close. So long as it has a finite mean and variance, the sample means will approach normality.

What would we expect?

Think about how you would have answered this question, before you knew the CLT:

…

Problem 1

The top-left and bottom-right squares on a chessboard are removed. Is it possible to cover the remaining squares with 1 × 2 (non-overlapping) rectangular tiles?

Problem 2

One random square on a chessboard is removed. Is it always possible to cover the remaining squares with (non-overlapping) 3-square L-shaped tiles?
(See image above for example.)

Problem 3

Choose 7 squares on a chessboard to cover with 1×1 square tiles. After each second, another tile is placed on an empty square if it shares at least two edges with tiled squares. …

This trigonometry quiz app was one of my first projects in Svelte. In this article I will highlight some of the key features of Svelte, and hopefully show how easy it is to get started with Svelte and build something cool.

Here is the HTML part of the main component, named <Gameboard/>. Note that it is inside a .svelte file, which will be rendered into HTML, CSS and JavaScript by the Svelte compiler.

The green capitalised tags <UnitCircle/>, <ProgressBar/> etc. are child components nested within the <Gameboard/> component.

The {#if} {:else} {/if} is Svelte syntax for conditional HTML markup…

D3 is great for creating interactive online data visualisations. It allows us to bind data to SVG elements (scalable vector graphics), then update and animate the SVGs when the data changes, or after user interactions.

Let’s start with the SVG markup for a circle element. The cx and cy attributes give the centre coordinates and r sets the radius.

I am an Australian teacher. My wife is a Chinese citizen. I was very surprised when she told me about a controversial new law in China to prevent high school students attending tuition schools on holidays and weekends.

Off-campus training institutions shall not teach curriculum subject-tutoring courses on national legal holidays, weekends and winter and summer vacations….
… the move is expected to ease the pressure on students undergoing compulsory education, reduce family expenditure on education and ease parents’ burden.
— Xinhua (Chinese government-run media agency)

The policy

This new policy has become widely known as the “double reduction” (双减) policy, i.e…

If you are into mathematics, it’s likely that you have heard of the Youtube channel 3Blue1Brown. But you may not have heard of the “Summer of Math Exposition”:

“A competition where anyone can submit a video, blog post, interactive game, or whatever else they dream up, and after the deadline we will select 5 to be featured in a 3blue1brown video” — https://www.3blue1brown.com/blog/some1

Over 1300 people submitted entries, including professional mathematicians, university students, high school teachers (like me!) and math enthusiasts of all ages. After the contest started, brilliant.org …

What does it take to reach the ✨number 1 spot✨ on the Top Writer list for a popular Medium tag?

Being new to Medium, I was interested in doing a little research.

• How often do these Top Writers publish?
• Which publications do they write for?
• What were their most popular articles?

Visualising data is my idea of fun! After selecting ten of these Top Writers and looking through their profile pages, I used D3.js to generate the colourful charts below.

The selected writers are arranged by number of followers. …

This article explains how I analysed data from the Medium website to answer the question: “Where are the articles in each Medium Topic published?”.

Here are the four key steps:

1. Inspecting the HTML
2. Parsing the HTML with Beautiful Soup
3. Creating Charts with Plotly
4. Generating the HTML for a Medium article

1. Inspecting the HTML

Clicking a topic on the Medium homepage takes you to a page such as https://medium.com/topic/math , which contains a list of the recent articles.

If we right-click and “Inspect” one of the articles, we find that each article is contained in a <section> tag.