Someone hands you a surface. One side is colored purple, and the other side is colored gold. You find that you can cut the surface along two disjoint loops and still have a single piece. But you can find no third loop to cut along without it breaking into two parts. Identify the surface, with a brief explanation.   This is from a mathematics topology course.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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Someone hands you a surface. One side is colored purple, and the other side is colored gold. You find that you can cut the surface along two disjoint loops and still have a single piece. But you can find no third loop to cut along without it breaking into two parts. Identify the surface, with a brief explanation.

 

This is from a mathematics topology course.

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