In some news item, it was pointed out that an Olympic gold medal is made with only 1% gold. Ok, that makes sense. A full 100% gold medal would probably be quite expensive. Also, gold is a rather soft metal so it might get bent or scratched too easily.

Let's get an estimate of the cost of a fully gold Olympic gold medal. To start, we need some of the dimensions of a medal. Thankfully, Wikipedia has a nice page with both the size and mass of medals for different Olympics years (of course they do). From this, the 2014 Olympic Gold Medal has 1 100 mm diameter and a 10 mm thickness with a mass of 531 grams.

I will assume that this is just a plain cylinder (which it probably isn't since it probably has some raised features to it). The volume and density for this medal will then be:

Using the listed dimensions, this gives a density of 6.76 grams/cm^{3}. This is much lower than the ^{3}^{3}density of gold with a value of 19.3 g/cm^{3}.

## If Not Gold, then What?

Now for the fun part. Let's say that the medal is 1% gold (by mass). What is the density of the rest of the stuff? To start, I will write the total mass of the medal as:

Hopefully it is clear that the *m* subscript represents the medal. I already know the mass of this other stuff in the medal, but I need its volume. If I subtract the volume of the gold from the total volume, that will just be the other stuff.

Now I can solve for the density of the stuff.

That's it. It's all finished except for the numbers. If I put the values from above into this expression, I get a stuff density of 6.717 g/cm^{3}. Based on this list of metal densities, it seems like that stuff could be several things. It's closest to the density of Cerium - but Wikipedia lists it as being both soft and it oxidizes in air. It could be cast iron or zinc. Modern pennies have a zinc interior, so maybe the medal is just like a huge penny.

## Cost of a Gold Medal

The gold medal has a mass of 531 grams. If it was 100% gold, it would have a mass of 1.52 kilograms. Damn. That's 3.35 pounds. You would surely feel that sucker around your neck. Wouldn't you?

Ok, but what about the cost? In my estimate of the gold that Smaug has under the mountain, I used a gold price of $49.5 per gram of gold. This would put the medal at a price of (just for the gold) $75,992.5.

Next question: why don't they make Olympic Gold Medals out of gold? I think the answer is obvious.

## A Historical Look at Medals

Sometimes I can't stop. Using the data from that Wikipedia page, I can plot the medal volume as a function of year (for both Winter and Summer Olympics).

Why did I add a linear fit? I guess just because I could. However, you can use it to answer the following questions:

- If both the Winter and Summer Olympic medals continue this trend, how big will the medals be around the year 2050?
- Could you get some type of exponential model to fit this data better than a linear fit?
- Why do the medals seem to get bigger over time? Is bigger better?
- I wonder if there is any correlation between medal size and location of the Olympics.

Go ahead and play with it. Plotly lets you try your own fits and make this into your own graph. That's what makes Plotly so awesome. Oh, I left off a couple of medals that weren't cylindrically shaped.

What about the medal density. There doesn't seem to be a trend for the density so I will just plot it as a histogram.

Look at the medal for Summer Olympics in 1912 with a density of 18.26 g/cm^{3}. That looks close to pure gold. Or maybe it's mostly lead.

One more homework question. How much would the 2014 medal be worth if it were made of Bitcoins? Yes, I know that Bitcoins aren't really real. That just means that you have to be creative to come up with an answer.