Explore natural cycles with a Moebius strip

Some things, like a story, have a definite beginning and a definite end – they don't repeat. Other things, like the seasons, don't really end. They change and return – every year there's another Spring. Things that repeat are cycles. There are many cycles in nature.

Here are two cycles related to global warming:

Air Cycle: Plants take in carbon dioxide and return oxygen to the air; humans and animals inhale oxygen and exhale carbon dioxide.

Carbon Cycle: When a living thing dies, carbon compounds remain in its body; decomposers release the carbon into the atmosphere as carbon dioxide; the carbon dioxide is taken in by plants; the plants form carbohydrates; a form of carbon returns to living creatures as they eat the plants.

A big problem related to global warming is that there is too much carbon dioxide that cannot be recycled quickly enough, so it builds up in the earth's atmosphere. Too much of anything in nature is not a good thing; the environment works because of delicate balances that cannot be disturbed.

In 1858 a German mathematician named August Ferdinand Moebius came upon a loop of paper with a truly astonishing property: it has only one side. The Moebius strip can be used to demonstrate how abiotic (nonliving) components are recycled, or used again and again in nature.

Start by cutting two strips about 2.5 cm wide from the long edge of a sheet of paper. Tape the two strips together to make one long strip. Make two long strips.

For each of the two natural cycles, write out the phrases below. Write side A phrases on one side of a long paper strip and side B phrases on the other side. Start side B phrases at the same end that side A phrases start, but write them upside down to side A. Phrases fill a side and are spaced equally from one another. The beginning of the first phrase on a side and the end of the last phrase should be slightly in from the ends of the strip.

For the Air Cycle: A – plants take in carbon dioxide; plants return oxygen to air. B – humans and animals inhale oxygen; humans and animals exhale carbon dioxide.

For the Carbon Cycle: A – living thing dies; decomposers release carbon into atmosphere. B – carbon dioxide taken in by plants; plants form carbohydrates; plants eaten by living creature.

Next, to make a Moebius strip, give a half turn to a strip of paper, as shown, and tape A to B.

Find the cycle's starting phrase and mark it with an X. Draw arrows from phrase to phrase until you complete the cycle. The Moebius strip has no beginning and no end, just as natural cycles involve a constantly repeating series of steps.

A Moebius Trick: Cut the Moebius strip down the center to create one very large loop. Each cycle in nature is part of the bigger world ecosystem.

Another Moebius Trick: Instead of making a half-twisted loop, give the strip one full turn before sticking the ends together. Then cut down the middle. The result is two interlinked loops. Each cycle in nature is related to other natural cycles. You can cut each of the two loops in half to make four interlinked loops. Try different twist and cut combinations.