Simson Lines - Whitman College
... There are several proofs available for the theorem, each having its own set of benefits and drawbacks. In this paper we present four proofs of Simson’s Theorem and one of its converse. We discuss the background needed to understand each proof, and each proof is accompanied by one or more figures ill ...
... There are several proofs available for the theorem, each having its own set of benefits and drawbacks. In this paper we present four proofs of Simson’s Theorem and one of its converse. We discuss the background needed to understand each proof, and each proof is accompanied by one or more figures ill ...
Constructive Geometry
... constructions. (For simplicity, we will not discuss the three-dimensional part of Euclid, contained mostly in Book 5). We consider the 48 two-dimensional constructions to be the world’s first systematic collection of algorithms. (We do not say, “the world’s first algorithms”, because there certainly ...
... constructions. (For simplicity, we will not discuss the three-dimensional part of Euclid, contained mostly in Book 5). We consider the 48 two-dimensional constructions to be the world’s first systematic collection of algorithms. (We do not say, “the world’s first algorithms”, because there certainly ...
Chapter 4
... angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. ...
... angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. ...
Homework Helper Lesson 3 Classify Triangles
... type of triangle formed by the easel and the desk according to its sides. Next, classify the type of triangle formed by the easel and the desk according to its angles. ...
... type of triangle formed by the easel and the desk according to its sides. Next, classify the type of triangle formed by the easel and the desk according to its angles. ...
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)