Hey all,

Found this on the internet and thought it was a little interesting. Did you know that the standard 12-hour clock is based around modular arithmetic? The day is broken up into two 12 hour parts. That means that the clock is based around modular 12 arithmetic. For example, If the time is 7:00 now, then 8 hours later it will be 3:00. If its 2pm, its really 2 mod(12) rather than 14 o'clock (unless you're in military time). However, even in military time modulo arithmetic is still used in the seconds and minutes which use modulo 60. Everytime the minute changes, rather than going on to 61, it starts again at second 1 of the new minute. The point is that we measure many things, both in mathematics and in real life, in periodicity, and this can usually be thought of as an application of modular arithmetic. Just thought I'd share

That's really interesting. So 12:00 means that minute-wise, we're at 0 mod 60. On a similar note, we use 60 as our base for minutes and seconds because of the influence of the mesopotamians, who based their number system in base 60 due to its large number of basic factors. Neat, huh?

I stumbled across this topic online as well. It's a pretty cool concept that I never really considered in relation to modular arithmetic. I really like the clock example because it is something that everyone is familiar with. If I were to ever teach a lesson to high school students involving modular arithmetic, I think that this would be a great example to use.

Here's an interesting applet for the clock problem, http://www.math.csusb.edu/faculty/susan/number_bracelets/mod_arith.html .

So I was thinking about other cycles in life that involve modular arithmetic, and all of the examples I could come up with involved time. At first, I thought of years, but then every fourth year is 366 days instead of 365, so years in general are not really mod 355. Then I thought about days of the week, like Sunday is 0mod7 and Monday is 1mod7. THEN I thought about a combination of the two and how I always figure out in my head what day of the week a certain holiday (mainly my birthday) is going to be on the next year. If there is a February 29th between my birthdays, it will be two days of the week later the next year, but if there isn't, it will be one day later. I have used this rationale in my head my entire life to figure out what day of the week things are going to be on a year later, but I think I always just kind of thought of it as a coincidence or something that just worked out. Really, it is 365mod7, which is 1, so there 7 goes into 365 52 times with a remainder of 1, making the day of the week 1 day later when there is 365 days in a year and 366mod7 which is 2 making the day of the week 2 days later if there is a leap year. Just so everyone knows my 21st birthday is on a saturday this year! YES and I used modular arithmetic to figure that out… haha