61–63 of 63 posts
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Yes. The better way to phrase it would be that some angles are impossible to construct, and importantly that includes a trisection of some angles that can in fact be constructed.
Interesting. So like you have rational numbers and irrational numbers, you have trisectable angles and non-trisectable ones.
Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
The "compass" and "straightedge" are (nowadays) just a colorful/concrete way to describe the problem. When mathematicians consider this, they phrase the conditions in such a way that no physical "compasses" or "straightedges" are involved. For example, you might say: (1) If you have 4 different points P, Q, R, S so that the lines PQ and RS are not parallel, you may "acquire" their point of intersection; (2) If you ha…
(a) implies (b) here, but I’m sure you know this.
From myself, I recommend Aluffi’s “Algebra. Chapter 0”, it’s more modern and I find its style much more matching my taste.
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Can't speak for ahelwer, but once at work we had to show (for certification purposes), that our program wouldn't get lost in an infinite loop. Now from a realistic standpoint, all they wanted was some evidence we had considered this possibility and some data/argument to show our confidence that it wouldn't. This was a simple program - you could confirm the algorithm wouldn't run forever by examining the code - look a…
In a company I worked for, systems were brought to their knees because of a while loop that went infinite under poorly tested conditions. There was a meeting and the head of the dev team came down to tell us that, in the meeting, it was decided that we should not use iteration any more because it runs the risk of going infinite. Instead, we should use recursion for all our looping needs. That was in a C# shop so of c…