Non-Orientable surfaces:
An orientable surface is orientable if it has two sides. The definition of a non-orientable surface is one on which there are regions that reverse an explorer's sense of right and left. A good example is the Mobius strip. The Mobius strip, also known as the Mobius band, is a surface that only has one side and only one boundary section. Because of the Mobius strip only having one side, it is non-orientable. You can easily make a Mobius strip with just a strip of paper. If you lay the strip of paper flat on a table, take one end and twist it. Now connect the two ends together and tape it. You now have a non-orientable shape of the Mobius strip. Even though it looks like it has two sides you can easily prove that there is only one. If you get a pen and place the tip on the Mobius strip, you can slide the paper underneath the pen without picking the pen up until the line connects.
After you analyze the line you will see the Mobius strip has one side making it non-orientable. Below is the definition of the Mobius strip “as the rotation of a line segment around a circle, with half twist. |
Mobius StripKlein Bottle |
Logic Puzzle DesignLogic Puzzle:
There is a water polo game with two teams; the Speedos and the Limbless. Who was on what team? Who drowned? 1. Mike threw the ball and scored when Peter was the golly. 2. Zach had no arms and no feet. 3. Ben enjoyed wearing his speedo. 4. Jose was on the winning team with Peter 5. When Ben played he was scored on by Jimmy. 6. Ling Hi Chin would help Zack play and was always holding on to him. 7. Juan’s tem did not have a chin. 8. Ling Hi Chin got hurt and could no longer play. 9. Jose subbed for Ling Hi Chin and did not stay next to Zach. 10. Mike liked having Juan play on his team. Q: Who was on what team? A: You know that mike threw the ball and scored on Peter, so they have to be on different teams. Ben enjoyed wearing his speedo, so you can assume he is on the team known as the Speedos. Jose was on the same team as Peter and they were on the winning team. You know Jimmy was scored on by Ben, which makes them be on different teams. Ling Hi Chin would help Zach play, so they must be on the same team. Jaun’s team did not have a chin, so Ling Hi Chin must not be on his team. Jose subbed for Ling Hi Chin when he was hurt, so Jose has to be on his team. Mike has to be on the team with Juan, because they liked being on the same team. Q: Who drowned? A: You know Zach had no arms and no feet, Ling Hi Chin had to leave the game and couldn’t help Zach any more and Jose did not stay net to Zach, resulting in Zach drowning, because how could he swim with no arms and no feet. |