Cite this!, thank you for pointing out that paper. We will cite it, and also I will read it!
fan_of_math wrote:
This result has applied to me in real life! My 3k pr is 8:43, which I ran back in college. At the time my mile pr was 4:43, slower than the average pace of my 3k (4:41/mile). Moreover, the overall pattern of the splits - went out hard, slower in the middle, closed hard - makes it possible that every mile-long subset of the race was slower than the race average. It's very interesting that I can be sure I broke my 1500m pr during this 3k based on IVT, but that I can't be sure about my mile!
That's really neat! It applies to me, too -- I ran 11:11 for the first two miles of a 5k when my 3k PR was 10:25, and I wanted to know if I ran some intermediate 3k of that 2 miles faster than 10:25, since at a constant pace my 3k split would have been 10:24.
Bad Wigins wrote:
Here is a realistic one you can do in your turkey trot 5k or your track:
1km 4:00
333 1/3 m 1:40
1km 4:00
333 1/3 m 1:40
1km 4:00
333 1/3 m 1:40
1km 4:00
total distance 5km, pace 21/5 = 4.2 minutes/k = 4:12/k
pace per any 1.333km segment = 5:40/1.3333 = 17/3 x 3/4 = 17/4 = 4.25 minutes = 4:15/k
Wow, nicely done! Elegant, and also totally reasonable to actually do in a race.
Maths are hard wrote:
If Keitany's HM was EXACTLY duplicated and put back to back (or in an infinite loop), then would there have to be a 12 km segment faster than Huddle's (spanning the 2 runs, if necessary)?
Yes. I can easily explain why using the analogous problem about functions that we use in the paper, but I'm having trouble coming up with a clear explanation in terms of running. I'll ponder it.
Borsuk-Ulam wrote:
I am thinking if her run was 'modular' (e.g. could take the last 4k and the first 8k) then we could always find a 12k section of at least average pace?
Yes, if you're willing to collect little bits of the run here and there such that the total distance of all of them is a mile, then you can definitely come up with a mile at exactly the average pace. Of course, if we allow that kind of thing, I can break the 4:00 mile; just allow me to do a couple dozen 50-meter sprints! :)