I’m deliberately ignoring actual units here, so you’ll have to think in terms of units of distance along the route and units of time for the simulation. Displaying the simulation Clearly, the two basic models we need for this are a bus and a bus stop. I spent a while wondering how best to connect the two together, and after coming up with some complex object graphs, decided that it would just be easier to keep a collection of each, and have each bus know how far it had gone along the route. We are at a bus stop. Get the index of the stop, so we can update in place (if we take on passengers)

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 Why Do Buses Come in Threes? is a delightfully entertaining ride for anyone wanting to remind themselves—or discover for the first time—that math is relevant to almost everything we do. Buses that bunch, identical potato chips, and slicing a cake evenly for an odd number of guests all have their links to intriguing mathematical problems. With great humor and a genuine love for the subject, the authors present the solutions to such conundrums as how fast one should run in the rain to keep dry and who was the greatest sportsman statistically. Those of us on the math side of the great cultural divide tend to be less enthusiastic about the power of intuition. One of the primary aims of this fun little book is to show how intuition often misleads us in questions that should be dealt with mathematically. A simple example is the probability that two people in a group of 23 will have the same birthday. It is not 23/365, the chances are actually 50%. 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.

It would be better if we have passengers arrive at any stops stops up to (say) five time units ahead of the current time. That’s more realistic, as people don’t generally turn up at a bus stop ages in advance. They normally aim to get there in enough time to make sure they don’t miss the bus.

PDF / EPUB File Name: Why_Do_Buses_Come_in_Threes_-_Robert_Eastaway.pdf, Why_Do_Buses_Come_in_Threes_-_Robert_Eastaway.epub 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, int stopIndex = busStops.Select((bs, n) => (bs, n)).Where(t => t.bs.Distance == bus.Distance).Select(t => t.n).First(); We are working on an approach which will ensure every member of the profession has access to a CPD process that is simple, flexible, and adaptable. No matter what area members work in, the integration of workplace learning with their CPD means CPD is valuable and relevant for everyone. The process is interactive, familiar, and responsive. 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.”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. 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.

I had to be honest: "No idea why they're assigning books for dumb adults to smart kids" was my first reaction, and I told her as much, but I had not read the book yet and I promised to revert once I had. 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?’ Passengers arrive at all stops right from the start, meaning that by the time the first bus gets to a later stop, there is a huge queue. You can see this in the simulation, which causes bus #1 to keep stopping, resulting in subsequent buses catching it up. You end up with a big cluster of buses at the end. It was the Sumerians who first decided they needed a zero. They counted in both base ten and base 60, and needed a symbol to indicate nothing in the 'tens' column, so that they could tell whether the answer was 123 or 23. But they didn't use this useful symbol to indicate the terminal digit, so out of context you can't tell 180 from 30, or from 3. 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’.The chapter headings are chosen to appeal to the child or the non-mathematician - 'Why can't I find a four leafed clover?', 'Why do clever people get things wrong?', 'why are showers always too hot or too cold?' and other intriguing problems that have been worrying us all our lives. Some of the contents are conundrums we've all ( well, nearly all) met before, such as the Konigsberg bridges, These things can help – but the ubiquity of bus bunching suggests that they can’t eliminate the problem altogether. 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). Rob Eastway has a book titled “Why do buses come in threes?” which is a collection of musings on the some of the mathematics behind some simple, and often common questions. The question that he used for the title of the book intrigued me, as his answer was (basically) that they don’t. They do come in twos (which he explained), but would probably not come in threes. This is a splendid little book. Frankly, I recommend it to everyone, but it would probably only really be appropriate for those who are math-curious. In my ideal world, that actually would include everyone, since there’s a huge difference between math-as-it-is-taught and all of the fantastic stuff that often makes math cool.