MATH ALERT: Country-Sized Medals
- Tyler Birschbach
- Aug 22, 2016
- 5 min read
The Olympics are over, and everyone can go back to not caring about table tennis, fencing and dressage (aka FANCY HORSE DANCING JUST KIDDING I TOTALLY STILL CARE ABOUT IT) . The medal counts have been tallied and once again the United States "win" the Olympics.
Some may argue that the point of the Olympics isn't to see which country is the best, instead that great athletes come from all countries. Which is true, and it is awesome to see so many athletes from around the world (if you weren't watching NBC Primetime Olympic Coverage which almost exclusively showed American athletes excel), but it is also pretty awesome to know that the United States came out on top again. Wouldn't it be awesome if the entire country got a gold medal for topping the podium for topping the podium? I don't mean each and every citizen get one, I mean one that the United States of America (and China and Great Britain) could wear. That's a big medal. But how big?
When figuring out the size of the country-sized medals, I took a few things into account: 1) the size of the real medals (diameter, thickness, etc), 2) the average size of the athletes that participated in the games, and 3) the average size of countries.
There are some issues with the measurements I selected, I'm sure, and there may even be some issues with the actual calculations (and if you care enough, please let me know and I will call you a nerd and promptly correct them). The average size of the countries is not just the average size of the countries that competed in the games. I could figure that out, but I am the one writing this so what I say goes. So here's what I found out.
The real medals are 85 mm in diameter, 8mm thick and weigh 500 grams.
The average athlete at the games is 1.77m tall.
The average country's area is 767,731 square km.
Here's where the math begins. To find out how big the medals would be for the countries, the ratio of medal size to athlete size needed to be found. The only issue now was finding the height and width to be used for the athletes to figure out the "height" for the countries. I split this up into two different measurements. There was the measurement that assumed that each athlete's area is made up of a square (which is false, except for some of the athletes I am sure). So the height and width of the country would be equal.
Here is the calculations for "square athletes":
With the average area of the country being 767,731 square km, that makes the height 876.202 km. The ratio for height of athlete to diameter of medal is 1.77m/0.085m meaning the athlete is 20.82 times taller than the medal's diameter. Using this, the diameter of the country sized medal would be 42.077 km, or roughly the distance of a marathon. Taking the area of a circle, the medal would have an area of 2,821 square km, or roughly the size of Samoa. Thanks to If It Were My Home.com we can see how big Samoa is relative to the United States, Great Britain and China.
(that's not the Great Wall being visible from space, which it's not, that's Samoa. China is HUGE)
Relative to the United States and China, the medal would be tiny. Like Michael Phelps receiving a pin for his 8,000th gold medal (neither the relative size nor his medal count were researched and are merely here for hyperbole). But these are still GIANT medals, taking into account the thickness of the normal sized medals (8mm), the country sized medals would be 3.96 kilometers thick. That means that the entire size of the medal (or Samoa in this instance) would be over 2 times taller than the World Trade Center.
But the athletes aren't squares, being rectangular (or most of the athletes at least), means the ratio between athlete height and medal diameter will be slightly larger. Here are the calculations for the "rectangular athletes":
In order to find out the ratio of width to height to use for the countries, I needed to find the ratio of shoulder width to athlete height for the Olympians. Finding the average for the actual athletes would require me to stop staring at pictures of the athletes on the internet and start staring at pictures of the athletes on the internet and holding a ruler up to the screen to measure their height and width. Instead I went with some guy named da Vinci's measurement of the ratios of man. In his drawing of the Vitruvian man (seen below),
he noted that the max width of the shoulders is 1/4 of the height. While this is in no means and exact measurement, it is an easy number for me to work with so I am going with it.
Using the same average area of the countries I found the new height of the countries to be 1,752.4052 km. This would mean the new diameter for the country-sized medal would be about 84.155 km (or roughly twice the size of the previous medal). (Insert more math here) and you find out that the new area is about 5,562.2 square kilometers, or roughly the size of Palestine. Again, I turned to my friends at If It Were My Home to compare the sizes of these countries to see how big our new medals are:
We are getting a bit bigger! The medal would actually kind of be noticeable on China now! The height of these medals, would be roughly 7.92 km, or only 1 km shorter than Mount Everest, and taller than all but 13 mountains in the world.
I attempted to use the areas and thicknesses of our new country sized medals to figure out how valuable a medal this sized would be. Unfortunately, the numbers I am working with here are ASTRONOMICAL (~60,000,000,000,000,000 kg) and my calculator didn't want to cooperate, so the rest of the measurements will be (even more) theoretical. The gold medals from Rio are reported to be worth about $620 (they are made out of sterling silver, with a coating of gold; if they were made of full gold each medal would cost about $23,000). Knowing that each medal is about .5 kg, we can see that they cost about $1,240 per kg, meaning our giant medal would cost a mere $74,400,000,000,000,000,000,000. Again, my math is probably way off on that, but we are also talking about a medal the size of a country and as thick as a mountain. Later this afternoon I might mock up some scale medals to award the countries, but who knows. Thanks for reading along.
Most fun mental image: A giant silver medal actually being created in China and randomly set down somewhere. They have enough room and enough money.
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