What’s in a number? This week: Pi

We all remember learning at school about the mysterious Pi – roughly 3.1416 – the number that connects the diameter to the circumference of a circle. 

This number crops up everywhere in maths and is mysterious enough to be the title of a 1998 film about a mathematician who suffers from chronic headaches and Chasidim vying to discover the number that will bring about the Messiah.

A value found in ancient Babylon (1900 BCE) was 3.125, and ancient Egyptians may have used 3.16 around the same time. Today, we know Pi more accurately – to 22,459,157,718,361 digits.

Surprisingly, the Tanach appears to give an inaccurate answer to Pi in the Book of Kings. 

Describing Solomon’s pool in the Temple, Kings I, 7:23 states that it was 10 cubits from one edge to the other, and 30 cubits in circumference. 

This yields a ratio of three, which is quite a way off. The Talmud (c500 CE) uses the same ratio for Pi, despite much more accurate versions being available.

Commentaries note the verse is not attempting to teach maths, and that this ratio of three is accurate enough for measures in Jewish law, such as when making an Eruv or a Sukkah. 

However, the Vilna Gaon says the Tanach has not got this wrong – and there is a more accurate approximation hidden within the verse. 

The word for circumference in Hebrew is ‘kavah’; however, in the verse, while it should have been written kuf-vav-heh, it is written just kuf-vav (kav) with the heh said but not written. 

The Vilna Gaon says that if you take the numerical value of kavah – 111, and divide it by kav – 106, and multiply it by the original ratio of 3 given in the verse, you get 3.1415. Indeed, a very accurate approximation for Pi!

Rabbi Garry Wayland is the former assistant rabbi at Woodside Park United Synagogue

 
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