Why Do Buses Come in Threes?: The Hidden Maths of Everyday Life

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Bus 1 leaves the bus depot to set off on its route. The driver has been held up and the bus is already a few minutes late leaving the depot. It then hits some unexpected traffic and by the time the bus reaches the first stop, it is several minutes late. I wondered how hard it would be to write a simulation to test this out. The simulation I describe here isn’t bad, but has (at least) three obvious shortcomings, which I didn’t really spot until the end. Although I’ve thought these through, I haven’t had time to try them yet, so this blog post will describe the first pass at the simulation (which is still quite interesting to watch). In real life, of course, there would be an intervention (Bus Two would almost certainly overtake, as soon as there’s room). And real life is messier than this model in other ways, too. Bus routes are served by more than two buses; passenger flows aren’t so evenly spread.

The animation is done simply by clearing the console and writing out the display for the current time period. The obvious way to do this wold be to call Console.Clear(), but this gives an IOException: _the handle is invalid._ Can’t remember the reason offhand, but LinqPad has a util function to do the same thing without the exception, so I call Util.ClearResults() at the start of each loop. Jules Gribble, Lesley Traverso and Caroline Stevenson offer an insight into their concurrent session at the 20/20 All-Actuaries Virtual Summit, ‘Are Actuaries Still Relevant?’ PDF / EPUB File Name: Why_Do_Buses_Come_in_Threes_-_Robert_Eastaway.pdf, Why_Do_Buses_Come_in_Threes_-_Robert_Eastaway.epub

But the book was aimed at neither yourself nor your friend's precocious son" I hear you say. It's a popular mathematics book and should be rated as such. The CPD committee is developing a vision for CPD in the future for the Institute. We are building on learnings from other actuarial and professional bodies in Australia and overseas. We are following established trails and seeking to take the best, for our profession, from their experiences. This is leading toward some changes, but the world is changing around us and we need to capitalise on that or be left behind. The main part of the simulation was a simple loop that kept going until the first bus reached the end of the route. The book identifies links between nature and mathematics, revealing how the subject rules and enhances our existence. Dotted throughout the book are practical uses for probability theory, applications of tangents while sight seeing, Fibonacci series, Venn diagrams in the predator-prey relationship, prime numbers, matrices and lots more to have you looking at numbers like you never did in school. Even geometry and trigonometry find their way in day to day situations we encounter, but we solve problems so subconsciously we don’t even realize those dreaded math concepts are at work. There is historical information, general trivia and a horde of interesting facts to help you learn and ponder as you read.

There is a chapter on numbers in biology - with Fibonacci, the golden ratio and a section on 'Pi and the circle'. It also explains why animals don't have wheels - which wasn't something I'd been worrying about. So the next time someone in your hearing asks why it is that buses all come along at once, you can reply, “mathematical inevitability”. You can see the full code for this simulation here. Copy the code and paste it into LinqPad, having set the language to “C# Statements.” Very well, then, here's my summary of where it ranks in that respect. If I had to give Timothy Gowers' "Very Short Introduction to Mathematics" or Conway's "Book of Numbers" a 5/5, then "Why do Buses come in Threes" deserves a 3/5. It explains and inspires far less than either, but it's not too bad.Our vision, our measure of success is when members say ‘I now see CPD as an integral part of my life, rather than a chore’. We also take a trip across the Atlantic to the culture of the Mayas, who had multiple calendars, and a symbol for zero which was a portrait of the god of death. Why multiple calendars? - Kaplan postulates a societal fear of an Ending, when the end of all the calendar cycles coincide - bringing a total End. Having many calendar cycles postpones this event for many years, and in the meantime, Why Do Buses Come In Threes?” delves into the hidden mathematics of everyday life. Those who find themselves fascinated by numbers and solve numerical puzzles as a hobby, will obviously love this book which sheds light of how maths is present anywhere and everywhere. And then there are people like me, who place mathematics on the same pedestal as foreign languages, because that’s how numbers float in front of us – no different from alphabets of a foreign script. The book serves to remind and help us discover how maths is relevant to everything we do, not just numerically. The author duo aims to provide new insights and stimulate curiosity. Bus One is now arriving at stops with populations bigger than some small Chinese cities. Bus Two, just behind, arrives a moment later to find them deserted. Without intervention, this situation will persist, essentially, forever. Spacing out three buses in the real world