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While I was taking a free walking tour in Sofia, Bulgaria, our guide pointed out what he referred to as the three layers of Sofia. I took a picture to capture them:
- At the bottom, you can see Roman ruins of Ancient Serdika from the 4th through the 6th centuries.
- In the middle, you can see the medieval Saint Petka's Church, which was constructed in the 11th century.
- And at the top, you can see part of the Presidential Complex, which was built in the 1950s.
It was amazing to see structures from over 1500 years apart all in one place, right next to each other.
The different buildings can be seen at different heights, or more accurately, different depths: the Roman ruins were only discovered when the city started digging to build a nearby metro system. The reason that the older buildings and ruins are located deeper is that as time goes on, more dust and debris settles on the ground, creating the ground level to rise. In several centuries, the ground will likely be even higher. And if someone were to dig deeper, they would likely find relics from centuries even farther back in time.
The question that I asked myself was the following: are the depths of the buildings proportional to their ages? If one artifact was twice as old as another, would it be found twice as deep? So I did a bit of estimations for the depths, compared to the elevation where the Presidential Complex is located, and this is what I found:
- Saint Petka's Church, which is approximately 900 years older than the Presidential Complex, was located at a depth of approximately 3 meters.
- The ruins of Serdika, which are approximately 1600 years older than the Presidential Complex, were located at a depth of approximately 5.5 meters.
Sample Problems
Sample Problems
1. Calculate the ratio of Saint Petka's age to Serdika's age, as well as the ratio of the depth of Saint Petka to the depth of Serdika. Are these ratios equal to each other? If not, how close are they?
2. Are the ages and depths relatively proportional to each other? If not, what might account for this?
3. If certain artifacts or ruins were found 11 meters below the current ground level, approximately how old would we expect those objects to be?
4. Our guide told us that the city of Sofia was first inhabited approximately 7,000 years ago. If artifacts from that time period still existed, approximately how deep should we expect to find them buried?
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