Asking here so as not to hi-jack the pizza thread. In that thread Grumman jokingly suggests cutting pizzas into 17 slices and provided a link to a cool animation of how to do it with a compass and straight-edge. I know I’m probably missing something obvious but after several viewings it seems the animated gif pulls this step out of its ass.
Two questions;
Yeah, I’m not seeing it either. But if all you want is a construction, this is much cleaner and fairly easy to follow. Of course, it’s also much different, so it won’t give you much insight into the original construction.
That particular compass length doesn’t matter. If you watch a little further, that arc is just used to quadrisect the angle a between the negative y axis and the cyan segment (giving a/4), then construct a 45° angle to get 45°-a/4 as well.
Note that even if the particulars of the construction are mysterious, the reason that it can be done is simply that cos(360°/17) can be expressed using only square roots; these are the only constructable numbers.
Okay, see it now. It was kind of confusing, though; they drew that arc about three times longer than necessary. So now that I can compare the two, the construction I found is effectively identical to yours.
EDIT: Also, while I was searching Wikipedia about the construction, I saw this article, and it made me LOL.
That animation is hilarious if you think about the pizza shop owner having to train his staff to slice pizzas that way.
Probably just be cheaper in the long run to invest in a CNC pizza slicer. Put the pizza on the table, select the number of slices or pattern and get your hands out of the way.
But that would only cut the pizza in 17 approximately equal slices: you need a straight edge and compass (and a perfectly circular pizza) to get 17 exactly equal slices.
Wanted: pizza chef at Luigi’s restaurant, on the corner of Maple and 5th Street. Must be punctual and willing to work weekends. At least three years previous experience as chef desirable.
Also, must have scored at least 700 on the Math SAT. Knowledge of Galois Theory a bonus.
*
Not to mention the human side of the story.
"The pizza is delivered to his customers tables and the hungry diners tear into their pies. Luigi sighs inwardly and wipes a tear from his eye knowing that not a single customer notices the mathematical precision that went into cutting 17 exactly equal slices of pizza. A custom that had been passed down in his family for generations.
Then one day a software engineer entered the restaurant and ordered a large pepperoni…"
Nonsense; you don’t need anything like the full power of Galois theory to do this. In fact, Gauss did it as a teenager around 40 years before Galois.
I had never seen the word “heptadecagon” before. Most people call it a 17-gon. What do you do for a 257-gon (which is also constructible).
Well then, that must be why Luigi regards it as a bonus. 
Oh, of course.
Well, Pizza Hut is pretty obliging with their special orders; maybe someone could see how they attempt the heptadecagon.
So is Domino’s
