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Research Triangle Project
Research Triangle Project
Complete view of each component as listed below.
Live interactive link:
Centroid:
Create your midpoints of each side (D, E, F) and draw medians from one side to the other. The intersecting point gives you the centroid.
Circumcenter:
Using the midpoints of each side, draw perpendicular bisectors from each segment. The intersecting point is the circumcenter.
Incenter:
Draw the angle bisectors from each angle (city). The intersecting point is your incenter.
Orthocenter:
Draw the perpendicular bisectors from each vertex to the opposing side. The intersecting points is the orthocenter.
The centroid is 12.94 miles from Chapel Hill, 9.63 miles from Durham, and 19.93 miles from Raleigh.
There are highways already constructed so they will need to resurface 42.5 miles. At $50,000 per mile, this is a total cost of $2,215,000.
The circumcenter is about 16.31 miles from each city.
There is a highway from Durham to the circumcenter, so for 16.31 miles, it would cost $815,000. For the other cities, 32.62 miles, it would cost $4,077,500. The grand total would be $4,892,500.
The incenter is 8.58 miles from Chapel Hill, 5.71 miles from Durham, and 25.18 miles from Raleigh.
Once again, these highways are already constrcuted. Only 39.47 miles will need resurfacing for a total cost of $1,973,500.
The orthocenter is 15.87 miles from Chapel Hill, 5.23 miles from Durham, and 30.67 miles from Raleigh.
There seems to be highways built, so re-pavement will cost $2,588,500 for 51.77 miles.
As seen above and using a simplified coordinate map, we plotted each city and constructed the triangle's four classical centers. Each center was evaluated as a potential site for a new professional baseball stadium. From there, using the distance formula, we calculated the total distances from each triangle center to the three cities. These distances were then converted into cost estimates based on the assumption that two-thirds of each route could use existing highways (costing $50,000 per mile) while one-third would require new construction (costing $125,000 per mile).
The analysis revealed the following total cost estimates:
Centroid: $2,215,000
Circumcenter: $4,892,500 (highest)
Incenter: $1,973,500 (lowest)
Orthocenter: $2,588,500
Based on these findings, the incenter emerged as the most cost-effective location for the stadium. This makes sense mathematically, as the incenter is equidistant from the sides of the triangle. Therefore, the incenter balances proximity while minimizing both new construction and total travel cost, making it the optimal location for development.
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