In this problem, my group (Me, Gabs Amon, and Carson Keeley), had to figure out how many people were in this space: It is a overhead image of Washington DC's national park during Obama's 2009 inauguration. Click here for the image in greater detail |
To figure this out, we followed some steps (outlined on the below poster):
1. Found measurements of the real life national park, and other landmarks in the picture, then measured the actual (printed) picture.
2. Created Scale: Scale: 656 ft./2.4 cm. = 273 ft./cm.
3. Figured out the size of a person: People are about 1.5 ft. by 1 ft.
4. Measured one of the blobs: 1.5 cm. by 2 cm. -> 1.5*273 by 2*273 -> 409.5 ft. by 546 ft. = 223,587 ft. squared
5. Estimated the amount of people in blob 1: 223,584/1.5 = 149,058 people in blob 1
6. Total Estimate: Our estimate: 149,058 people in blob 1 * 10 blobs = 1,490,580 people in all
Here is a poster that goes into more detail about this:
1. Found measurements of the real life national park, and other landmarks in the picture, then measured the actual (printed) picture.
2. Created Scale: Scale: 656 ft./2.4 cm. = 273 ft./cm.
3. Figured out the size of a person: People are about 1.5 ft. by 1 ft.
4. Measured one of the blobs: 1.5 cm. by 2 cm. -> 1.5*273 by 2*273 -> 409.5 ft. by 546 ft. = 223,587 ft. squared
5. Estimated the amount of people in blob 1: 223,584/1.5 = 149,058 people in blob 1
6. Total Estimate: Our estimate: 149,058 people in blob 1 * 10 blobs = 1,490,580 people in all
Here is a poster that goes into more detail about this:
Habits of a Mathematician used:
In my group, we used two habits of a mathematician. Solve a simpler problem, and visualize. Both of them because of our unique approach to the problem. We solved a simpler problem when we chose to just measure one of the blobs, and multiply that answer by the amount of blobs in all. Basically, we only had to calculate one blob's area and how many people were in it, because we just estimated the rest. We visualized by drawing out the problem, and using whiteboard marker on the original image (it had been laminated) to figure out our thoughts.
By the way, there were actually 1.8 million people there. Our estimate was about 1.5 million.
In my group, we used two habits of a mathematician. Solve a simpler problem, and visualize. Both of them because of our unique approach to the problem. We solved a simpler problem when we chose to just measure one of the blobs, and multiply that answer by the amount of blobs in all. Basically, we only had to calculate one blob's area and how many people were in it, because we just estimated the rest. We visualized by drawing out the problem, and using whiteboard marker on the original image (it had been laminated) to figure out our thoughts.
By the way, there were actually 1.8 million people there. Our estimate was about 1.5 million.