Conjecture Rubber Sheet Geometry

This site constitutes our final project for math 5337 computational methods in elementary geometry taken at the university of minnesota s geometry center during winter of 1996 this course could be entitled technology in the geometry classroom as one of its more important objectives is to provide students presumably math educators with a wide variety of activities.

Conjecture rubber sheet geometry.

Menu geometry proof conjecture. A conjecture is an educated guess that is based on known information. For 11 15 show each conjecture is false by finding a counterexample. President to be inaugurated.

Topology is sometimes called rubber sheet geometry because exact sizes and shapes don t matter. Make a conjecture about the number of students who will participate in the robotics competition this year. If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30 th day as well. To change the network you must either break a connection or add one.

There are 526 students in the school this year. It is sometimes described as rubber sheet geometry since there is no notion of distance. In contrast cutting and then gluing together parts of a space are bound to fuse. Three points on a plane always form a triangle.

Kennedy is the youngest u s. From a topologist s perspective there is no difference between a bagel and. To understand the conjecture think of two dimensional spaces like the surface of a football or of a doughnut. Since allowed deformations are like manipulating a rubber sheet topology is often called rubber sheet geometry.

A circle can be stretched into a square with a rubber band but you can t stretch a figure eight into a circle without tearing it. He was a founder of topology also known as rubber sheet geometry for its focus on the intrinsic properties of spaces. The most basic problem in topology is to determine when two topological spaces are the same that is they can be identified with one another in a continuous way. As long as the map is topologically accurate the exact design does not matter.

For example a coffee mug with a handle and a doughnut are deemed to be the same because we can deform one into the other without any tearing. Rubber sheet geometry topology does not distinguish between a circle and a square but it does between a circle and a figure eight. The popular term is rubber sheet geometry. It is the study of the properties of an object that do not change under continuous deformations such as stretching and bending but not tearing.