## Wednesday, August 6, 2014

### Math is easy!!

"Mathematics is the music of Reason" --James Joseph Sylvester

Most runners I know are pretty good at math.  Better than your average American.  Why?  Well, if you are anything like every other runner, you do math while you run:
•  "....okay, one mile into today's run, 7:43 passed, looking to run 7 miles today.....carry the 4, divide by 60......I started at 4:30......I'll be done by 5:24!"
• ".....10miles today, rest tomorrow, 6miles on Wednesday.....trying to get 50 in this week, Saturday is gonna have to be huge!"
• ".....9hours into this thing, 39miles gone....boy, only leaves me a few hours to get that last 11miles...."
And, if you have been paying attention during your running career you'll probably have noticed that most shorter races are measured in the Metric System. We all have ran 5Ks, 10Ks, 100m, 400m, etc.  But, with the establishment of the current marathon distance, in 1908, of 26.2 miles, we now have longer races measured in miles.  Marathons at 26.2miles, Half-Marathons, of course, at 13.1miles, 50M, 100M, etc.  Then, to confuse you a bit more, we throw in races for the ultrarunning community of  50K and 100K.

The inner geek in me enjoys mathematics.  I may not understand a lot of it, but I'm good at it, and can do some fairly large calculations on the fly.  Many, many, many hours of pounding the pavement have been spent keeping occupied by doing math in my head (if nothing more than counting cadence).

So, this is a short blog, pointing out the beauty of math as it applies to running.......

Everyone know what the Fibonacci Sequence is?  Well, quick definition:  The Fibonacci Sequence is a sequence of numbers (starting at either 0 or 1), where each subsequent number is the sum of the previous two.  So, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.  Easy enough, right?

Now, have you heard of the Golden Ratio?  Well, the math can be confusing, but basically, it's a rule of mathematics where two numbers have a ratio that is equal to the ratio of their sum to the larger of the two numbers.  The Golden Ratio is 1.61803.

Now, take the numbers of the Fibonacci Sequence and compare their ratios:
• 3/2 is 1.5.....5/3 is 1.667.....8/5 is 1.6.....13/8 is 1.625
If you keep going, the ratios of the Fibonacci Sequence are quickly approaching the Golden Ratio.

Now, back to running......almost every runner knows that 1 Mile = ~1.6Kilometers.  The actual ratio is 1:1.6093.  Notice something?  That's right.....the ratio of Miles:Kilometers is almost exactly the Golden Ratio.

Take what you've learned to this point now and head back to the Fibonacci Sequence.  Pick a number in the sequence, let's say '13'.  Your number is in Kilometers.  The preceding number is that same distance, in Miles (in this case, '8')!!  Go ahead, check it out.
• Your friend says he's running an 8K race this weekend.......Ask him, "What's your best 5-mile time?"
• You're at a track meet and they announce the winner of the 3K having a time of 8min.  You can exclaim, "Wow.....4minute miles!"  (3K=2miles, 8/2=4)
• You are trying to tell your German foreign exchange student that you ran a half marathon this weekend.  "Yeah, I ran 21K this weekend.......it was no biggie."
OK, OK, enough 'geeking out' for one day.  Next time you are out for a run, though....maybe you stretch that 10K afternoon run into a 13K, just to make it 'Fibonacci Compliant'!

Or, just slap those headphones back on and forget everything I just said........