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Almost all of what I write below is fairly self-evident to anyone with some basic geometrical reasoning, and while the precise details require trigonometry, the concepts could probably be explained to a bright eight year old. But even so, it took until after I was thirty before I reasoned the whole thing out, and saw the implications of applying the geometry of circles to seasonal change.

If you were to draw out a circle, your pencil would be, at the very top of the circle, moving purely from side to side. When your pencil is at the side of the circle, it is moving purely up and down. As it turns out, half of the upward movement of a circle takes place in the third of it closest to the middle. And, if we take a circle up a dimension and make it into a sphere, an identical pattern emerges. On a sphere, half of the surface area is between the north and south 30th parallels. The exact trigonometry of this is something that is left as an exercise to the reader, but it is a pretty simple extension of the intuitive concept that at different points on a circle, you are moving in different directions.

So, to bring us to the second part of our title, seasonal change. Seasonal change occurs because the earth is tilted on its axis, and as it travels around in its circular orbit, different parts of its globe are highlighted by the sun. As the earth moves to different positions in its orbit, the arc inscribed by the sun across the sky changes, and since that arc is a product of the geometry of the circle of the earth's orbit and the sphere of its globe, that arc follows the basic geometry of circles. And what that means is that half of the change in the amount of daylight takes place within a month on either side of the equinox. In the northern hemisphere, daylight will increase rapidly from February 20th to April 20th, and then slowly increase up the summer solstice, slowly decrease from then until August 23rd, when it will decrease rapidly until October 23rd, after which it will decrease slowly until the winter solstice, after which it will increase slowly until February 20th, and then our cycle begins again.

In other words, there are four months of the year when the amount of daylight changes the most dramatically. The other eight months have relatively minor changes in the amount of daylight. This is not really that extraordinary of a finding, although there are several reasons why it took me three decades to figure it out. A small part of this has to do with the fact that, (as someone has probably already noticed, and decided to correct me on), the earth neither has a circular orbit, nor is the earth a sphere. The earth is slightly pear shaped, and travels around the sun in an ellipse with an apogee and a perigee, although these do not make a great difference. More important is the fact that the changing arc of the sun's course across the sky is not all that apparent from many places on the earth: at or close to the equator, it is negligible, and even past the line of the tropics, it is not immediately apparent. Only getting close to the 40th parallel does the change in daylight start to be noticed as a dramatic change. Also, the change of daylight can often be obscured by atmospheric phenomena like clouds. And depending on location, the change in daylight might not immediately be reflected in the weather. I think one of the main reasons why I never figured the pattern out was because I grew up in the Pacific Northwest, where the moderating effects of the Pacific Ocean were a more important factor in determining climate than the amount of daylight.

So, as with just about every other aspect of geology, much of seasonal change is based on some fairly elementary principles of geometry, which are then distorted almost beyond recognition by the vagaries of chemistry and geography.

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