Using Pythagoras to be more efficient.
As a high school student with a keen interest in Mathematics, I’ve always been trying to find the most efficient way to travel from class to class around my high school. Finally there is a practical use for the Pythagorean Theorem! Lets discuss…
For anyone unaware Pythagoras was a Greek Philosopher. I’m not going to delve into that part of his life (frankly I don’t know anything about it), but what we will be discussing is his amazing discovery! One that every high schooler will be very familiar with. If you are familiar with the Pythagorean Theorem then you can gloss over the next paragraph.
The Pythagorean Theorem states that in any right triangle (A triangle with one angle of 90°) the sum of the squares of the lengths of the 2 sides not opposite the right angle (a²+b²) equal the square of the length of the hypotenuse (c²). Wow that’s quite a mouthful! The image below might help explain a bit better than I can:
What we also know is that:
a + b >c
We can then use this idea to travel more efficiently.
A Practical Example
At my high school we have buildings on either side in a U-shape. In the centre is the school hall and an open air quad area.
Lets say I want to travel from the red point to the blue point. Well I have a couple options:
- You could walk towards the bottom side of the building, across and back up the other side. (The Green Route)
- You could walk diagonally through the quad area. (The Purple Route)
Do you see it? Try imagine the right angled triangle in your head.
In this case the paths do not form a triangle, but it is quite obvious that the most efficient route is the purple route.
Some other things to consider
Of course this idea does not apply in all cases. The example given above is in a 2D space. In the real world we have to consider the additional annoying third coordinate, the z-coordinate.
Lets say the red point and the blue point are on the third story of the building. If you were walking the purple route you would have to find the nearest stairs, walk down to the ground floor walk across the quad and then back up another flight of stairs on the other side of the building. Whereas taking the green route you can remain on the same floor, avoiding any stair climbing. In most cases we can safely assume that the green path is more efficient as going up and down stairs is not only tiring for lazy teenagers just trying to get to their next lesson, but is also a longer distance to travel.
Another extremely important thing to consider is congestion. You are not the only high schooler trying to get to class.
Lets say the red point and blue point are on the ground floor and there is an event happening in the quad area. In this case no flights of stairs will be needed to travel from the red point to the blue point on either route. In this case is it tricky to say which route would be more efficient. You could take the purple route and breeze through the event in the quad without being slowed down or you could be stuck trying to get past hoards of people at the event.
In this case I would take the green route. Yes it is longer, but I know that I won’t get stuck trying to push past people. It’s the risk I am willing to take.
In Conclusion
Next time you are walking through your office or are at school, try this technique. It may sound silly, but it works surprisingly well and finally gives a practical use for the Pythagorean Theorem.
