Lesson Plan 1
... Geometry the sum of angles of a triangle is 180. 3) States to the students that in Hyperbolic Geometry the sum of the angles of a triangle is less than 180. Show some examples. 4) States to the students that in Hyperbolic Geometry, all the axioms for neutral geometry hold, but the parallel postulate ...
... Geometry the sum of angles of a triangle is 180. 3) States to the students that in Hyperbolic Geometry the sum of the angles of a triangle is less than 180. Show some examples. 4) States to the students that in Hyperbolic Geometry, all the axioms for neutral geometry hold, but the parallel postulate ...
Absolute geometry
... Under the correspondence ABC ↔ XY Z, let two sides and the included angle of ABC be congruent, respectively, to the corresponding two sides and included angle of XY Z. That is, for example, AB ∼ ...
... Under the correspondence ABC ↔ XY Z, let two sides and the included angle of ABC be congruent, respectively, to the corresponding two sides and included angle of XY Z. That is, for example, AB ∼ ...
Non-Euclidean geometry and consistency
... Do these make sense?! They do if we imagine space is like the surface of a sphere! 1. All perpendiculars to a straight line meet at one point. 2. Two straight lines enclose an area 3. The sum of the angles of a triangle are grater than 180° ...
... Do these make sense?! They do if we imagine space is like the surface of a sphere! 1. All perpendiculars to a straight line meet at one point. 2. Two straight lines enclose an area 3. The sum of the angles of a triangle are grater than 180° ...
Curves and Manifolds
... theory of plane curves of degree 3 is already very deep, and connected with the Weierstrass's theory of bi-periodic complex analytic functions (cf. elliptic curves, Weierstrass P-function). There are many questions in the theory of plane algebraic curves for which the answer is not known as of the b ...
... theory of plane curves of degree 3 is already very deep, and connected with the Weierstrass's theory of bi-periodic complex analytic functions (cf. elliptic curves, Weierstrass P-function). There are many questions in the theory of plane algebraic curves for which the answer is not known as of the b ...