# Is there a name for this polygon? **URL:** \ **Category:** Factual Questions\ **Created:** [August 30, 2025, 4:34pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604 "2025-08-30T16:34:31Z")\ **Posts on this page:** 13\ **Page:** 3
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [September 4, 2025, 4:42pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/41 "2025-09-04T16:42:51Z")
> [@MrDibble](#): > > Which is all about the marked line. In the real world, that’s going to be a ruler. Going from memory, you use a straightedge then mark it at a specific intersection. That’s not the same as using a ruler. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [September 5, 2025, 5:17am UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/42 "2025-09-05T05:17:15Z")
That’s no different than using a specific measurement on the ruler (which is how we did it). ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [September 5, 2025, 9:42am UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/43 "2025-09-05T09:42:51Z")
I think the issue some have with neusis construction is that it isn’t intrinsically precise. You need to slide the marked ruler so that, by eye, a marked distance intersects a desired element. There is an intuition that an ideal compass and straightedge is infinitely precise. But sliding something about doesn’t, for want of a better phrase, “lock in”, in the same way. Very hand wavy. Neusis construction isn’t limited by the precision of the markings made on the ruler, these can created with compass and straightedge along with the rest of the construction. The trick is that distances on a straight line so inscribed can’t be arbitrarily lifted up and slid about without it becoming a neusis construction. But complaining about this is perhaps best left to the ancient Greeks. ---
**Author:** ![Frodo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frodo/32/302_2.png) [@Frodo](https://boards.straightdope.com/u/Frodo)\ **Post date:** [September 5, 2025, 1:52pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/44 "2025-09-05T13:52:24Z")
As the saying goes, there are no bad Pizzagons nor bad Sextangles… ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [September 5, 2025, 6:51pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/45 "2025-09-05T18:51:39Z")
You can make the reference circle for trisecting using neusis any size, so you can set your compass to line up exactly with a specific mark on the ruler just as easily. So it’s as precise as the compass is (which, let’s face it, is never going to be 100% either) ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [September 8, 2025, 2:24pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/46 "2025-09-08T14:24:42Z")
> [@MrDibble](#): > > That’s no different than using a specific measurement on the ruler (which is how we did it). Yes it is because a ruler has gradations whereas (theoretically) a neusis is infinitely precise. Show me where π/4 is on a ruler. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [September 8, 2025, 4:20pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/47 "2025-09-08T16:20:42Z")
> [@Saint\_Cad](#): > > Yes it is because a ruler has gradations whereas (theoretically) a neusis is infinitely precise. The specific trisect neusis uses an _arbitrary_ circle. So it can be _precisely_ X ruler ticks in radius. > [@Saint\_Cad](#): > > Show me where π/4 is on a ruler. Show me the relevance of π/4 for the trisection method. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [September 8, 2025, 4:36pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/48 "2025-09-08T16:36:39Z")
There is a difference between making a mark on a straightedge at a specific point and using a premarked straightedge. > [@MrDibble](#): > > The specific trisect neusis uses an _arbitrary_ circle. So it can be _precisely_ X ruler ticks in radius. Let the [vertex](https://proofwiki.org/wiki/Definition:Vertex_of_Angle) of α be labelled B. Let A be the point of one of the branches of α such that the distance AB equals pq. Let the other branch of α be extended past B through D. Let a [circle](https://proofwiki.org/wiki/Definition:Circle) be drawn with [center](https://proofwiki.org/wiki/Definition:Center_of_Circle) at B with [radius](https://proofwiki.org/wiki/Definition:Radius_of_Circle) AB. Let the [straightedge](https://proofwiki.org/wiki/Definition:Straightedge) S be placed so that: S passes over A p lies on the [circle](https://proofwiki.org/wiki/Definition:Circle) at C q lies on the [straight line](https://proofwiki.org/wiki/Definition:Straight_Line) BD at D. Show me where in this construction you can make a circle so that you a guarantied that in the last step that the intersection _C_ is at one of the premarked points on your ruler. Proof taken [from here](https://proofwiki.org/wiki/Trisecting_the_Angle/Neusis_Construction) if a visual is needed. To do what you are claiming (just use a ruler) it would have to have both constructible and non-constructible numbers on it. For example, do rulers have the root of cubic polynomials on them? > [@MrDibble](#): > > Show me the relevance of π/4 for the trisection method. How about cos 20 degrees? ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [September 8, 2025, 4:49pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/49 "2025-09-08T16:49:22Z")
> [@Saint\_Cad](#): > > Show me where in this construction you can make a circle so that you a guarantied that in the last step that the intersection _C_ is at one of the premarked points on your ruler. If you don’t understand that pq can be any _arbitrary_ measurement and is equal to AB = CD\*, I can’t really help you. Maybe this will help?: [![](https://upload.wikimedia.org/wikipedia/commons/9/97/Angle_trisection_archimedes.png) ](https://upload.wikimedia.org/wikipedia/commons/9/97/Angle_trisection_archimedes.png) If I use ten ticks on a marked ruler as my pq, then CD is going to be ten ticks. If I use 20, it’ll be 20. I’m not using the markings on the ruler to _measure_ anything. I’m using them as the delineators of my neusis marking. **Which all the rest of the construction uses as its basis.** You do understand that the proof you linked to _starts_ with a measurement on the ruler, right? You know, the bit you somehow failed to copy, from the start of that proof: > Let there be a [neusis ruler](https://proofwiki.org/wiki/Definition:Neusis_Ruler) S marked by two [points](https://proofwiki.org/wiki/Definition:Point) p and q. > [@Saint\_Cad](#): > > How about cos 20 degrees? What about it? You didn’t answer what the relevance of the first one is, this second one is equally irrelevant. ---
**Author:** ![vbob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vbob/32/4439_2.png) [@vbob](https://boards.straightdope.com/u/vbob)\ **Post date:** [September 9, 2025, 11:05pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/50 "2025-09-09T23:05:57Z")
> [@scudsucker](#): > > My math teachers were really, really big on practical understanding of maths before venturing into the … uh… harder part, where irrational numbers exist. That sounds very rational. I was lucky enough to have an irrational math teacher. I might even have had an imaginary math teacher. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 9, 2025, 11:13pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/51 "2025-09-09T23:13:27Z")
“Imaginary numbers” is a terrible term for them. They should be called “rotational numbers”. All i is, is a left turn. Really, that’s it. If you’ve ever made a left turn, you’ve used imaginary numbers. “i^2 = -1” just means that if you make a left turn, and then make another one, you’ve turned yourself in the opposite direction from where you were going before. ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [September 9, 2025, 11:20pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/52 "2025-09-09T23:20:15Z")
> [@Chronos](#): > > But hey, you can take that as an opportunity. If nobody else has come up with a term for something, you can do so yourself. Quick, ask ChatGPT what a good name would be! /S ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [September 10, 2025, 12:23am UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604/53 "2025-09-10T00:23:21Z")
> [@Chronos](#): > > “Imaginary numbers” is a terrible term for them. They should be called “rotational numbers”. My vote is for positive numbers to be called “forward numbers,” negative numbers to be called “backward numbers,” and imaginary numbers to be called “sideways numbers.” [Previous page](https://boards.straightdope.com/t/is-there-a-name-for-this-polygon/1022604.md?page=2)