This blog of the National Museum of Mathematics not only records highlights of many of the math tours given by the Museum over the years, but but includes ideas and processes used to create those tours, as a resource so that you can create tours, too. So the first idea to get across is that you indeed can create tours that will help other people perceive the mathematics that infuses the world around and that is nearly ubiquitous. All it takes is a genuine love of mathematics, and opening your own eyes to see the mathematical connections and ramifications that surround us every day.
The first several posts go through a number of the key elements and aspects that underlie essentially any tour. You can create a tour in almost any setting, indoors our outdoors, suitable for rain or shine, and with topics suitable for any target age range/mathematical background. Once you dive into this, you will find that the question becomes not “oh my gosh, how will I find anything to say?” but rather “Wow, how can I ever pare this down to a one-hour tour?” A few key principles lay the groundwork for a successful tour, and we will highlight those first, in the next several postings. With some care and a bit of practice, you will be able to keep tour participants rapt with the wonders of mathematics.