Related papers: Compass Constructions
It is well-known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from the ancient times that these constructions can be performed when it is allowed to…
In this short paper we show that with a small change of the common ruler and compass construction of the regular pentadecagon, we can produce more regular polygons
The purpose of this paper is to prove that every finite set of points that can be constructed in the Euclidean plane by using a compass and a ruler can also be constructed by using unitary match-sticks in a non-simultaneous way and…
In this paper we discuss Chasles's construction on ellipsoid to draw the semi-axes from a complete system of conjugate diameters. We prove that there is such situation when the construction is not planar (the needed points cannot be…
We present several ruler and compass practical geometric constructions that can be performed in the lemniscate curve. To be precise, we provide recipes for halving, doubling, adding, subtracting, and transferring lemniscate arcs with ruler…
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
We study the problem of construction of a triangle from the feet of its internal angle bisectors. It is proved that in general case ruler-and-compass solution of this problem is impossible.
In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the…
We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction…
We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a…
Euclid's reasoning is essentially constructive. Tarski's elegant and concise first-order theory of Euclidean geometry, on the other hand, is essentially non-constructive, even if we restrict attention (as we do here) to the theory with…
In 1888, Heinrich Schroeter provided a ruler construction for points on cubic curves based on line involutions. Using Chasles' Theorem and the terminology of elliptic curves, we give a simple proof of Schroeter's construction. In addition,…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…
Our goal is to present, in what we believe is the most efficient way possible, a construction of four mutually tangent circles.
A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.
In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many applications of mechanical engineering, civil engineering and…
We give a simple proof to the fact that it is impossible to use straightedge and compass to construct a triangle given the lengths of its internal bisectors, even if the triangle is isosceles.
Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search…
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.