Compass Constructions

Arman Margaryan; Nerses Aramian

RECORD

Compass Constructions

Arman Margaryan, Nerses Aramian

History and Overview · Submitted 12 Oct 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively.

how it is stated · asserted 1.00 read the record →

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Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,705 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.30 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first constructing circles or lines and then considering their intersection. This hints us a way to approach the problem, which is possibly the most straightforward approach. However, the execution of it is rather interesting and worth the effort. The approach that we are talking about is to show that the intersection of circles and lines, lines and lines can be constructed using only compass. The intersection of two circle comes in as trivial given, since all we need to do is construct circles in this situation. Our task can be formulated even more precisely. Suppose we are given four points A, B, C and D. Our task is to show that the intersection of lines AB and CD can be constructed using only compass, and that the intersection of AB and the circle centered C and passing through D can be also constructed using compass.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively.	contribution 0.73	0.60	0.93	asserted 1.00
s1	If we are using compass and ruler the way we construct new points is by first constructing circles or lines and then considering their intersection.	background 0.94	0.12	0.02	asserted 0.98
s2	This hints us a way to approach the problem, which is possibly the most straightforward approach.	method 0.52	0.24	0.02	hedged possibility 0.90
s3	However, the execution of it is rather interesting and worth the effort.	background 0.36	0.18	0.02	asserted 0.94
s4	The approach that we are talking about is to show that the intersection of circles and lines, lines and lines can be constructed using only compass.	method 0.92	0.42	0.11	asserted 0.99
s5	The intersection of two circle comes in as trivial given, since all we need to do is construct circles in this situation.	method 0.49	0.23	0.03	asserted 1.00
s6	Our task can be formulated even more precisely.	method 0.58	0.31	0.02	unclear 0.74
s7	Suppose we are given four points A, B, C and D.	method 0.50	0.18	0.02	asserted 0.57
s8	Our task is to show that the intersection of lines AB and CD can be constructed using only compass, and that the intersection of AB and the circle centered C and passing through D can be also constructed using compass.	contribution 0.56	0.39	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first constructing circles or lines and then considering their intersection. This hints us a way to approach the problem, which is possibly the most straightforward approach. However, the execution of it is rather interesting and worth the effort. The approach that we are talking about is to show that the intersection of circles and lines, lines and lines can be constructed using only compass. The intersection of two circle comes in as trivial given, since all we need to do is construct circles in this situation. Our task can be formulated even more precisely. Suppose we are given four points A, B, C and D. Our task is to show that the intersection of lines AB and CD can be constructed using only compass, and that the intersection of AB and the circle centered C and passing through D can be also constructed using compass.

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