Construction Of Polygons Research Articles

A Construction of Regular Polygons of pq Sides Leading to a Geometric Proof of rp - sq=l

The construction of 15, 51, and 85 sided polygons is an interesting exercise when studying ruler and compass constructions. The method is based on the famous Greatest Common Divisor theorem that if p and q are relatively prime, there exist counting numbers r, s such that rp-sq= 1. The proof of this theorem, while elementary, involves descent, and working back through a messy chain of equations. The spirit of the algebraic steps is quite different from that of geometric construction. Hence it is interesting in a geometry class to use a proof less dependent on an algebraic lemma. Indeed, a proof of the lemma falls out as a corollary.

A Construction of Regular Polygons of pq Sides Leading to a Geometric Proof of rp - sq = 1

A Construction of Regular Polygons of pq Sides Leading to a Geometric Proof of rp - sq = 1

The Division of Angles into Equal Parts and Polygon Construction

The Division of Angles into Equal Parts and Polygon Construction

The Division of Angles into Equal Parts and Polygon Construction

The Division of Angles into Equal Parts and Polygon Construction

Drobnosti z konstrukcí pravidelných mnohoúhelníků

Drobnosti z konstrukcí pravidelných mnohoúhelníků

On the Trisection of an Angle and the Construction of Regular Polygons of 7 and 9 Sides

On the Trisection of an Angle and the Construction of Regular Polygons of 7 and 9 Sides

On the Trisection of an Angle and the Construction of Regular Polygons of 7 and 9 Sides

On the Trisection of an Angle and the Construction of Regular Polygons of 7 and 9 Sides

Note on the geometrical construction of certain polygons

Note on the geometrical construction of certain polygons

On the Functions Defined by Differential Equations, with an Extension of the Puiseux Polygon Construction to these Equations

On the Functions Defined by Differential Equations, with an Extension of the Puiseux Polygon Construction to these Equations

Practical Plane Geometry and Projection for Science Classes, Schools, and Colleges

A VERY practical and useful book by an experienced teacher: it is designed to meet the requirements of students at the Royal School of Mines, at the Royal Military Academy, at Cooper's Hill, and elsewhere, and embraces great part of the two higher stages of the Science and Art Department syllabus. There is no great scope for absolute novelty in such a work, and our author acknowledges his indebtedness to the works of many, if not most, of his well-known predecessors, but the arrangement appears to be judicious, and the constructions good and clearly enunciated. In the Practical Geometry (six chapters) the student is taught the use and construction of scales, of triangles and polygons, and there are numerous problems on areas, on circles in contact, and on other plane curves with their tangents and normals. The orthographical portion treats of the projection of the five regular solids, of other simple solids, of flat and curved surfaces, intersected by cutting planes, and of solids inscribed in, or circumscribed to, the surfaces of other solids; of the interpenetration of solids, of the projection of shadows, on isometric projection, on the solution of the spherical triangle, and on horizontal projection—a very extensive and varied bill of fare. In addition there are numerous questions for practice, many of which are taken from examination papers, and the text is illustrated by several clearly-drawn figures. Part ii. contains eighty-one large-page plates to further illustrate the constructions. The two parts together ought to enable any painstaking student to take a creditable place in his examination and to acquire a solid acquaintance with the subject.