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January 2026 saw a large number of weather stations achieve record maximum temperatures in Australia, particularly in New South Wales, South Australia and Victoria between Jan 26 and 31. The map below shows the large region of Australia with an average maximum in excess of 45°C during the last week of January (map under Creative [ ]
In this post we consider the problem of how many rectangles (including squares) there are in a staircase grid of size , made by stacking rows of unit squares as shown in the figure below for . Place coordinates on the grid so that the bottom left is at . Then we shall add up [ ]
Since this post in 2016, Earth has continued to warm, with 2023 and now 2024 set to exceed 2016 as our hottest years on record. The table below shows that every month now has a maximum anomaly at least 1.5°C above the 1850-1900 baseline (data from here). Month Maximum anomaly relative to 1850-1900 baseline (°C) [ ]
Imagine a car or truck speeding away in front of you on the road. Here is a rough method to estimate its distance and speed using your outstretched hand (try this as a passenger, not a driver!). At any given time its distance away is approximately We use the figure below to estimate angles based [ ]
Below is a list of some statistics related to performances across test series. They are current up to 15 February 2022 31 December 2024. Data is from ESPNcricinfo. Most series playing 5 or more tests: AR Border (AUS) 15 RB Kanhai (WI) 14 IVA Richards (WI) 14 AJ Stewart (ENG) 13 GS Sobers (WI) 13 [ ]
We present here a calculation of the location of a star as a function of its declination, the observer s latitude and time after it is at its highest position in the sky. We use the fact that stars trace out circular paths about a fixed point in the sky. The image below shows a celestial [ ]
I have created a few interactive charts with Tableau on winning/losing/drawing international men s cricket streaks using data from ESPNcricinfo.com s Statsguru. You can click on any of the links or graphs to interact with it in a new page. 1. Most consecutive tests played with N matches of a given result (won/lost/drawn) 2. Fewest consecutive tests [ ]
In this post I would like to prove the following identity, motivated by this tweet. The first of these equalities is straightforward by the definition of binomial coefficients. To prove the second, we make use of partial fractions. We write the expansion where the coefficients are to be determined. Multiplying both sides by for some [ ]
Adding to my earlier blog post about the highest proportion of test scores above m after n innings, I have created some new interactive charts for best streaks early and mid-career in both bowling and batting in tests and ODIs. The data is mostly from https://data.world/cclayford/cricinfo-statsguru-data. 1. Test batting Most runs in at most n consecutive [ ]
In this post we find the largest parallelogram, rhombus, rectangle and square that can be contained in a given triangle. We will see that in the first three cases we can achieve half the area of the triangle but no more, while it is generally less than this for a square. 1. The largest parallelogram [ ]