**Steven Walker, OCR Maths Subject Advisor**

National Pi Day is informally celebrated by mathematicians around the world on March 14 at 1.59. If you’re not happy about the American date format then feel free to come back to this blog on 22 July for Pi Approximation Day. However, Pi is more than just the ratio of the circumference of any circle to the diameter of that circle, and in this blog I will look at a few of the ways Pi may feature across the curriculum.

### History

We know that the properties of a circle were studied in Ancient Greece by Archimedes, so it seems likely that this was of interest across the ancient world. Archimedes used Euclidean geometry to show that the area of a circle is equal to the area of a right-angled triangle with base length equal to the circumference of the circle and height equal to the circle radius (see this example using Desmos).

He also used the difference between perimeters of circumscribed and inscribed polygons to find the circumference. You could try this yourself using dynamic geometry software, such as this example using GeoGebra.

The Bible makes mention of the measurements of a basin in 1 Kings 7:23 with mention later of thickness which has been suggested gives an approximation for Pi as 3.10 . Look for the references yourself to confirm this estimate.

### Engineering

The electro-magnetic spectrum, which includes light, radio waves and X-rays, travel as waves that follow a sine curve. The 360 degree scale to define a full rotation is an arbitrary scale, but the 2Pi radian scale is based upon the angle subtended by an arc of a circle equal in length to its radius.

Radians are used because it makes it possible to relate linear measurements directly with angle measurements. This is demonstrated quite easily by plotting the curves *y =* sin *x* and its inverse *y =* sin^{-1}*x* on the same axis using graphing software (for example this sine curve graph using Desmos). Change between radians and degrees to see the visual difference when working with equal scales on the *x* and *y* axis.

Since calculations for wavelengths and frequency use radians rather than degrees, an understanding of Pi is needed for accurate work.

### Space

Circular motion uses radian measurements of angles in the calculations for the orbit of planets and the estimation of distances using data collected from telescopes, so the use of Pi is important for calculations in the context of space exploration.

It is interesting to note that whilst the distances considered in space travel are vast, it has been suggested that using an accuracy of Pi to only 15 decimal places is sufficient for NASA calculations. Why not consider the accuracy of your calculations using different approximations of Pi?

### Computing

The ability to calculate Pi to increasing accuracy and/or at a faster speed is one way to claim the prize of best computer. A team at Google calculated Pi to 31.4 trillion digits in 2018, but this was beaten in 2020 by a cybersecurity expert in USA with Pi to 50 trillion digits calculated in 303 days. The record now stands at 62.8 trillion digits, calculated in just over 108 days, by a team from Switzerland.

### Drama and music

Mnemonics such as “May I have a large container of coffee?” are used to remember the value of Pi by representing each digit by a word with the same number of letters. Students compete on stage to recite Pi to the greatest degree of accuracy. The current record is held by an Israeli teenager set in 2022 for correctly repeating the first 2022 decimal places of Pi.

A search on YouTube yields a number of songs using the digits of Pi for the lyrics, and even converting the digits to a musical scale to play on instruments.

### Stay connected

Are you doing any special Pi themed lessons? Share your ideas in the comments below. If you have any questions you can email us at maths@ocr.org.uk, call us on 01223 553998 or tweet us @OCR_Maths. You can also sign up to subject updates to keep up-to-date with the latest news, updates and resources.

### About the author

Steven originally studied engineering before completing a PGCE in secondary mathematics. He has taught secondary maths in England and overseas. Steven joined OCR in 2014 and has worked on the redevelopment of OCR’s Entry Level, GCSE (9-1), FSMQ and A Level Mathematics qualifications. He now focuses mainly on supporting OCR Level 3 qualifications at work whilst at home helping his daughter with her early introduction to mathematics in primary school.