Conjecture Rubber Sheet Geometry

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.

Conjecture rubber sheet geometry.

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. Since allowed deformations are like manipulating a rubber sheet topology is often called rubber sheet geometry. Any transformation of an object on a rubber sheet resulting from stretching or bending is considered to be the same object as long as the sheet isn t ripped. 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.

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. Menu geometry proof conjecture.

The popular term is rubber sheet geometry. Rubber sheet geometry topology does not distinguish between a circle and a square but it does between a circle and a figure eight. He was a founder of topology also known as rubber sheet geometry for its focus on the intrinsic properties of spaces. There are 526 students in the school this year.

President to be inaugurated. Elastic sheet of rubber it could be stretched and compressed but every detail would remain intact. The con guration of a network points connected by various lines is a topological property. To change the network you must either break a connection or add one.

From a topologist s perspective there is no difference between a bagel and. 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. As long as the map is topologically accurate the exact design does not matter. It is sometimes described as rubber sheet geometry since there is no notion of distance.

Make a conjecture about the number of students who will participate in the robotics competition this year. To understand the conjecture think of two dimensional spaces like the surface of a football or of a doughnut. A conjecture is an educated guess that is based on known information. 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.