Originally posted by Rictor
Alright, call me stupid, but I can't figure it out.
The rise/run of both is exactly the same, as is the area of each individual component, and yet there is a whole square less in one than in the other. It is concievable that the position of the elements could produce this discrepancy, but then the overall area would not be the same.
The rise over run is NOT the same.
Consider the following fact: if you use a horizontal or vertical line to slice any right triangle, the resulting smaller triangle will be congruent to the larger in all respects.
Now take the three triangles we have: red, green and the whole triangle. The green one is 3/8. The red one is 2/5. The whole triangle is 5/13. There is no way you can find a linear relationship between the rises or the runs here. If you were to take the sine or cosine of the non right angles of each of these triangles, you would discover that they do not match up--which they should, because of congruency.
So, in the end, the "hypoteneuse" of the large triangle actually bows out in one picture and bows inward in the other, at exactly the point where the red and green triangles meet.
