Round and round, here we go again.

29/03/2012 § 1 Comment

It honestly isn’t something one thinks about on a daily basis but if one does bother to put some thought into it, they might realise that trig cycles exist almost everywhere in life, in little bits and pieces. To quickly define a cycle, really a cycle could be anything that occurs or happens in life as long as it starts from somewhere, gradually gets to the end and starts over again. For example, a bicycle wheel is a cycle because, say, if you make a red mark on the wheel, it will constantly turn again and again as the bike moves. That is a kind of cycle that is needed in order to move the machinery.

Let’s think about how important cycles are in reality. Cycles of life, cycles of nature, mechanical cycles, human cycles, etc. Cycles exist before their purpose is to keep something functioning. If we think about a simple piece of machinery such as a windmill (actually not that simple, in reality), its main purpose is to keep the propellors turning and turning so that energy could be generated or in order to mill grain. The windmill is a kind of cycle and all cycles turn for a purpose and in order to accomplish a task. Without these certain tasks people would have a deficit and deficiency of certain things, in this case, milled grain or less wind-generated energy. In this case, such cyclic and trig behaviours are quite important in life. Other important cycles that I think about more than others include for example the Sannomiya bus’s route, sometimes I think about my breathing, and since I like stars, I sometimes think about how the moon orbits the earth and how are solar system orbits the sun and that makes me happy.

More importantly, I constantly think about my every day life cycle – wake up, get ready, do school, do activities after school, go home, do homework, eat dinner with family, do more homework, procrastinate, do more homework, procrastinate, do lots of homework and sleep. And repeat. I think almost all students experience this never-ending cycle.


There are numerous kinds of cycles one can think of in a single sitting. There are big cycles in our environment such as the water cycle (precipitation, evaporation, condensation) and the cycle of our solar system. Some include the cycle of a clock’s minute or second hand (or even the hour hand), a train or bus route (the Rokko Liner or the Sannomiya bus route), the turning of a windmill or a wheel, and even intangible and unseeable things. These include the cycles in our body, for example our digestive and respiratory system as well as our blood circulation. There are other systems in the body that are cycles but aren’t really appropriate for a school blog. Here is where I ask people to use their imagination and knowledge of health and sex education.


The difference between these types of cycles is basically only that you can see and/or touch some of them while others kind of hang there in existence but you can’t quite touch it — just like time. Time is a 24-hour cycle that we experience every single day but it’s intangible. All cycles however are similar in that they start at one place, end at another but resume from the very beginning.

Because cycles can be different and somewhat intangible in certain cases, it’s important to measure some of them. The changing seasons of Japan is a cycle for example and can be measured in temperatures, humidity, percentage of rain and, basically, anything related to weather. Time is also measured from seconds to days to years to centuries to millennia. We measure these cycles because we need to keep track of how much progress those cycles have been making. The accuracy of our measurements differ depending on the type of cycle. Between keeping track of time and keeping track of how many times a toy train has been circling its track to entertain a child, obviously the measurements of the time is far more vital than that of a toy. Mathematical models and measurements come into play when the cycles become bigger topics that cover a lot more ground, such as things in astronomy (the solar system), biology, the weather and mechanics.

The frequencies and periods of different cycles also differ depending on how big of an impact it makes on our lives. Some can also be unpredictable and spontaneous. Economic cycles can have long or short frequencies and periods as well as global warming and the green house effect. Smaller and more irrelevant cycles such as the turn of a bike wheel, a ferris wheel, a music box, different turns in Monopoly and other littler things have shorter periods and frequencies.

And now that I think about it, we really are surrounded by a heck of a lot of cycles. You wouldn’t even know that they’re cycles until you kind of stand still for a while and think about it. And then, “Oh my god, no way.”


§ One Response to Round and round, here we go again.

  • eadurkin says:

    I really hope you enjoy writing posts such as these, Kari. I want you to know that I thoroughly enjoy reading them: not just because of the cool images and personality you put into the blog – which are fantastic, but also because of the depth of thought and expansive array of ideas that are explored here.
    My favourite quote (from a mathematical perspective) in this post is “We measure these cycles because we need to keep track of how much progress that cycle has been making”. That is such a succinct and accurate understanding of the whole idea of measuring cycles. (An English teacher might criticise the inconsistency between plural in the first part and singular in the second, though.) I definitely could not have stated that idea better myself, and will be quoting that sentence as I teach trig in the years to come.
    Thank you for the rich thoughts.

    More detailed feedback and level of achievement will be posted on Moodle and Gradebook within a week.

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