Unwrapped Standards: G.CO.10 - Prove theorems about triangles
... Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoni ...
... Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoni ...
Unit 7 – Polygons and Circles Diagonals of a Polygon
... Participants will now investigate the exterior angles of a polygon. It is often difficult for students to understand intuitively that this sum does not depend on the number of sides of the polygon. Participants may use the polygons that they have already constructed to study exterior angles for the ...
... Participants will now investigate the exterior angles of a polygon. It is often difficult for students to understand intuitively that this sum does not depend on the number of sides of the polygon. Participants may use the polygons that they have already constructed to study exterior angles for the ...
Chapter 5: Poincare Models of Hyperbolic Geometry
... kγ for any k 6= 0. The group PSL2 (C) is isomorphic to the group of fractional linear transformations. Remember that we wanted to classify the group of direct isometries on the upper half plane. We want to show that any 2 × 2 matrix with real coefficients and determinant 1 represents a fractional li ...
... kγ for any k 6= 0. The group PSL2 (C) is isomorphic to the group of fractional linear transformations. Remember that we wanted to classify the group of direct isometries on the upper half plane. We want to show that any 2 × 2 matrix with real coefficients and determinant 1 represents a fractional li ...
1 Reteaching
... Two other conditional statements can be formed from the hypothesis and conclusion. Inverse: This is formed when the hypothesis and conclusion are negated. Contrapositive: This is formed by both exchanging and negating the hypothesis and conclusion. ...
... Two other conditional statements can be formed from the hypothesis and conclusion. Inverse: This is formed when the hypothesis and conclusion are negated. Contrapositive: This is formed by both exchanging and negating the hypothesis and conclusion. ...
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.)