The Elliptical Race Track Stadium

Eshan Abbas

1st post. 1st Math Write-up. An Original.

Human has had always the desire to take advantage of everything it has around since the beginning. From the trees to the careers around, we always are getting a proof for it. And that’s a great thing to see.

But unfortunately, there’s a negative side to it. Nowadays, we are seeing a great increase in the number of accidents, social crimes, anti-social activities, and more, but I wouldn’t like to say all of them.

Anyway, I will focus on only a few of them.

In today’s world, what I have seen is that with development, there has been a subtle, significant decrease in free space for children, and walking space for those who want to. Moreover, a day will come when the big stadiums will also be consumed in the name of development.

So, I am bringing the concept of a new stadium, in counter to the above, and also to the normal race tracks – The Elliptical Race Track Stadium.

Here’s a 2-D model of the ERTS –


The ERTS, as seen above in the 2D figure, will be an elliptical stadium. I have shown one entrance and one exit in the figure, but that doesn’t mean that we cannot have more entrances and exits for the easy coming and going of the people. Inside the stadium, there will be two points, S and F, which can be used as the starting and the finishing points respectively. There will be several paths, and all of them will have S and F as their common points.

Now, for example, let us consider a 100 m race. Any racer will start from S, go in any straight path such that he or she touches the edge of the ellipse at any point, and then reach F. There will be temporary poles at each point the players reach the edge, so that they may grab the pole with one of their hands, and use the rotational motion to turn about the pole and get on running again.

Likewise, there are several more uses, but I will focus on them later.

The ERTS works on the following property of the Ellipse:

The sum of the distances from a point on the ellipse to its two foci always remains constant for every point on the ellipse.


In the above figure, the bold statement simply states that CA + CB = constant = major axis length, where A and B are the foci of the ellipse and C is an arbitrary point on the ellipse.

Since infinite lines can pass through points A and B, therefore theoretically, there are infinite paths possible from A to B. And the distance from A to B in all these infinite cases will always be the same, which is equal to the length of the major axis of the ellipse.

In other words, we can say that whatever may be the path of the traveller, if he or she starts from any of the two foci, touches the edge of the ellipse and comes back to the other focus, the distance travelled will always be the same.

Realising this, I thought of this stadium.

Now, I will come to the comparison of the ERTS with the normal stadium.

First, I will focus on the normal race tracks.


A normal race track looks like the one above. It is a combination of a rectangle and two congruent semicircles, whose diameters are equal to the shorter side of the rectangle.

Now coming to the racing part again, we see that players take positions not at the same starting point, but different starting points according to the distance of the track from the centre. They have the same finish point though.

Alright, you might have got the idea about both the ERTS and the normal race track.

Now, consider these questions:

  1. How much accurate is the distance of each starting point from the finishing line?
  2. How much accurate is the turn of all the tracks? Are they even circular?
  3. Doesn’t the one who is the farthest track have the least speed while covering the circular path and so on?

There are several more questions like the above.But that will be a waste of time. So I directly go on to shows the advantages of the ERTS over the normal race track:

  • It can be built in a smaller area when compared to a circular stadium or the normal stadium. It can be even built inside the normal race track!
  • The normal race track can accommodate a limited number of runners at a fixed time. But we can accommodate infinite number of runners in ERTS, theoretically.
  • Every runner can start from the same point, which ends the procedure of fixing different starting positions for different runners.
  • The ERTS can be built much more accurately than the normal stadium. The tracks can be built too more accurately, since we have to fix straight lines only.
  • The ERTS can also be used for marathons in the near future, since we can have infinite paths to run on.
  • The ERTS can be used for jogging, and calculating how much distance we have run quickly.
  • The ERTS can also be used to learn riding vehicles.

The ERTS can be used as a maze, if we ever get in a tough situation. The ERTS though has some disadvantages:

  • Since there are sharp edges, therefore there’s a high chance that one may meet an accident if he or she is riding a vehicle or running.
  • There’s a high chance of cheating in the racing competitions.
  • Players may collide with each other when they are reaching the finish point.COUNTERMEASURES: To counter them, we can apply the following:
    • Having cameras set up at the intersection points to prevent cheating.
    • Modifying the sharp edges to smooth turns.
    • Having well defined paths with enough protection barriers, if needed.

Overall, the ERTS has an advantage over the normal stadiums. Also, with the free space decreasing day by day, we are in a need now to upgrade our technology as per our convenience. This stadium has a great potential, if we use it wisely.

I hope that you all readers of this blog like my idea and my project. I am still working on its subtle aspects. If you have anything useful to say regarding my idea, please do mail me at

2 thoughts on “The Elliptical Race Track Stadium

Add yours

  1. I think this is a great idea, at the very least as a way to reinforce the constant sum property of ellipses, not to mention as an alternative to the traditional racetrack. I have one question – you say the constant sum is equal to twice the length of the major axis. In Canada, since we define the major axis as the greatest distance between any two points on the ellipse, that constant sum is equal to the length of the major axis. Do you define the major axis differently?


    1. Sorry, my bad. Actually, we learnt that as CA + CB = 2a, where a is half of the major axis length. Anyway, I edited the blog wherever I felt necessary. THANK YOU FOR IDENTIFYING THE MISTAKE.


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