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Splitting a triangle

Published online by Cambridge University Press:  23 January 2015

Russell A. Gordon
Russell A. Gordon*
Affiliation:
Mathematics Department, Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362-2083 USA
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Let T be a triangle and let A be the area of T. Given a point p inside the triangle and a number r that satisfies 0 < r ≤ ½, we seek to count the number N (p, r) of straight lines that pass through p and cut T into two pieces so that one piece has area rA. As the point p and the ratio r vary, the value of N (p, r) ranges from 0 to 6. Given a ratio r, we want to determine the regions within T for which the function N (p, r) assumes various integer values. For example, a region inside T for which N (p, r) = 6 only exists for values of r between and ½, and we would like to quantify the area of this region (as a fraction of the total area of the triangle) as r varies.

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Articles
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The Mathematical Gazette , Volume 97 , Issue 540 , November 2013, pp. 474 - 493
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Copyright © The Mathematical Association 2013

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References

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