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Number 12: Can you calculate the angles of a dodecagon?

Let's meet the largest number that has just one syllable (single-morpheme). Take it away 12.


Working out the angles of a dodecagon​

The Australian 50c piece is our only non-round coin. With 12 equal sides it is what we maths nerds call a regular dodecagon*. Here is a cool way to work out the size of each of the 12 angles on such a shape.

  1. Choose a corner of the dodecagon and draw a line from that corner to each other corner of the figure. This will split your dodecagon into 10 triangles.

  2. We know from about year 8 (I know – a long time ago!) that the angle sum of a triangle is 180 degrees. And we can see that the angles of all these triangles perfectly cover all the angles inside the dodecagon.

  3. With this, we realise the sum of all 12 angles must be 180 x 10 = 1800 degrees.

So each corner on your 50c piece is a 150-degree angle! * do – two, deca – ten, gon - sides


Cutting your time in half​


We don’t really know why our day is split into 24 hours, but we do that clocks splitting day and night into 12 hours each date back as far as Ancient Egypt and Mesopotamia. The Romans also used a 12-hour clock. Some of the earliest mechanical clocks displayed all 24 hours of the day, but these were hard to read. Simplicity and cost saw 12-hour clock faces become the norm. One advantage of a 12-hour timeface, as opposed to a 10- or 20-hour day, is that 12 hours is easily divisible into 3 parts (4 hours each) and 4 parts (3 hours each) without splitting hours into minutes. Cute time fact – look at any advertisement for a watch and the time is almost always something around 10:10 am/pm. The theory is that evenly spacing the hands on either side of the 12 creates a symmetry that best shows off the watch.


Did you know?​ Enjoy these fascinating numerical facts about 12!


Who wants to be a trillionaire? There are 12 zeroes in a trillion and some experts believe that the current growth of new industries and ongoing consolidation of extreme wealth will soon lead to the world’s first trillionaire. At the same time, in recent years as the United States has approached its debt ceiling, some economists have proposed minting a single coin worth … $1,000,000,000,000.

You’re ribbing me! The normal human body has 12 pairs of ribs. However, about 1 in 200 people are born with an additional rib or pair of ribs called cervical ribs. These awesome anomalies attach to the 7th cervical vertebra in your neck. At the front, they might be attached to the typical first rib by fibrous tissue, or they could just “float” at the front.


Months in an ancient year The ancient Roman calendar contained not 12, but 10 months. This included a winter period of an unfixed length, causing early Roman years and seasons to fall completely out of sync with the real world. Sometime around 700 BCE, the Roman ruler Numa Pompilius replaced the winter doldrums with two additional months, January and February, bringing the total number of months to the modern 12.


INSPIRATIONAL THINKERS & DOERS Briane Greene - astrophysicist


Recently I hosted astrophysicist extraordinaire Briane Greene, renowned for ground-breaking discoveries in superstring theory – most notably the co-discovery of mirror symmetry and of spatial topology change. Huh Adam … spatial mirror what? Essentially Brian asks deep questions about the fundamental components of matter – at the very smallest level what is the universe made of and what forces drive it? Not surprisingly, Brian’s work has captured the imaginations of people around the world, with his appearances on the Late Show with Stephen Colbert and the Joe Rogan Experience racking up millions of views. He’s authored six incredibly successful books, is head of Columbia University’s Center for Theoretical Physics, and chairman and co-founder of the World Science Festival. He’s even starred as himself on the popular Big Bang Theory TV series. String theory is pretty deep stuff. Many of the ideas in string theory involve there being more dimensions to the universe than the 4 dimensions (3 of space and 1 of time) that we perceive. One of the most popular theories suggest we live in an 11-dimensional universe. Of the 12 signs of the zodiac, Brian and I both happen to be Aquarians. Fair to say we both believe in the potential of an 11-dimensional universe far more than we do astrology! #LoveMyJob

Gremlins in number 011 trivia

​Apologies for the omission of a crucial word in our maths puzzle in number 011. I asked for “the largest number not expressible as the sum of two composite numbers”. As a few astute readers pointed out, there is no largest such number, the list is infinite! This led to a hasty addition of the crucial word even to the problem. If instead we look for the largest such even number, the answer is 38. Well done Tama Cooper and Tim Marsh! Ok Adam, win them back with an awesome prize! The good people at Think Inc who brought Brian Greene to Australia are about to tour the amazing cosmologist Neil deGrasse Tyson. And I have 4 double passes to give away for shows in Adelaide, Sydney, Melbourne, Brisbane or Perth from July 4 to 11! If you’d like to watch me cuddle up again with one of the world’s great minds, send your best joke about mathematics, physics or the universe to number@adamspencer.com.au by 5pm AEDT Friday 28 April 2023. I’ll share the winning jokes in my next newsletter and across my socials if you tell me your social handle too. Or, you can always simply buy tickets here. Yours in numbers, Adam

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