WT60: Acute and obtuse triangles

[Toxie207]

This is fascinating. I have an honours degree in mathematics - though my area of interest was primarily functional analysis. Thanks for your videos. Can I ask, when we say s3(ob) iff s1 + s2 =< 1, should we not just make the inequality strict? That way we have no ambiguity? Sorry if the answer is obvious! Keep up the great videos.

[njwildberger]

Hi Toxie207,

Thanks for the good question. The issue is: should a sector formed from two perpendicular lines, ie a right angle, or a spread of 1, be considered to be acute, obtuse, both or neither? I am inclined to the answer: both.

This is a symmetric solution, similar to the idea that the number 0 is both positive and negative.

[grichard24]

This video stopped at around 6:16 and would not go any farther.