Athletics (100 m)

In the introductory post of the series, I discussed how I was quite hyper and energetic as a child; one of the positive ways that this energy manifested itself was in the track events. From the ages of 8 to 11, I participated in sprints and relays and won gold and silver medals in both individual and team events.

Here, I will analyse the 100 metre (m) track that used to be drawn on my school playground for Sports Day. The structure of this post differs significantly from the Four Corners post - I am not looking at the math behind the running of the race; rather, I am focusing on the math behind the design of the track.

In all honesty, it would have been a treat if my math teachers at school could have used such examples to make geometry and the Pythagorean theorem come to life when I was younger...

My school playground

The figure above shows a simple top view sketch of my school. In the figure below, I have focused on the available playground area and included its dimensions too as these are integral to how the track was drawn for the sprint events.

Track length and design

You might be thinking - "Why not just use the length of the right side of the field? After all, it is exactly 100 m!"

That didn't work for multiple reasons.

• First, one end of the track would have been too close to the trees and boundary wall and the other would have been practically touching the playing field entrance gate.

• Second, since the boundary wall was inclined, ensuring all 6 tracks were of the same length would have required starting some distance away from the boundary and this would have shortened the track.

• Third, tents used to be put up for parents and teachers in the canteen area, volleyball and basketball courts and cycle stand sections (refer the first diagram) and laying the track towards the other end would have made viewing the race a challenge! 😅

So, what are the other options? Let us consider them using the labelled figure below.

AE

Since starting the track at corner C would not be feasible for reasons discussed earlier, let's say that we start from E, about 15 m from the boundary/tree wall. By Pythagoras' theorem in the right-angled triangle ABE:

AE² = AB² + BE²

Using AB = 55 m and BE = 85 m, AE comes out to be ~101 m which appears to be a great way of laying the track.

However, this turned out to be impractical because the lower left portion of the playground:

• was rather uneven, stony and too close to the stage and

• housed the victory stand that was used throughout the Sports Day as it was in close proximity to both parents (for them to view) and the stage area (for announcers)

BD

The track couldn't start at B and end at D because D is too close to the seating area and there wouldn't have been enough space to create a finish line.

So, the track would have to start at D and end at B. By Pythagoras' theorem in the right-angled triangle ABD:

BD² = AB² + DA²

Using AB = 55 m and DA = 80 m, BD comes out to be ~97 m which falls slightly short of the required length.

So, what did my school do?

Well, the additional 3-4 m were added by extending the track a little past the playing field entrance. This was achieved by opening the gates fully so that they lined the walls. This was less than ideal from a viewing standpoint as potentially the most exciting part (i.e. the end of the race) would not be clearly visible to the spectators. However, there was no other practical or mathematical alternative so my school opted for the only workable solution!

Reflections from writing this post...

My first reflection (or realisation) was how I had never once stopped to question or consider how the track that my school drew on Sports Day each year was, in fact, 100 m. Only while researching this post did I uncover the mathematical reason behind it!

Second, such a real world example can be intelligently used in a lesson plan by a teacher to illustrate the power of constraints and how they guide our decisions. So many decisions that we take as adults are shaped by constraints that are a part of our lives - be it practical, emotional, social or financial.

Lastly, writing this post brought back a ton of happy memories connected with school and Sports Days! 😃 On that note, here is a photograph of me on the victory stand with my gold medal from the 100 m race in 5th standard... yes, some of us clearly look much better as children than as adults! 😂