My interest is that I am bringing an Algebra intervention back to market: http://tiltontec.com. I’d love your feedback if you have the time to check it out.

Keep up the good fight! 🙂

-ken

]]>Why do the daylight hours follow a sinous curve (number of daylight hours is a sinous function of time)?

From the point of view of a stationary earth, the effect of its orbit is that the sun orbits the earth. Changing that point of view to one where both the earth and the sun are stationary, the earth’s axis can be seen as wobbling such that the poles follow circular paths into and then back out of the sunlight. The poles’ change of position in the dimension of the axis between the circle’s two solstice positions would be the movement into and out of the sunlight. The shadow line would fall along the axis between the two equinox positions. The rate of change of daylight hours would be greater between mid-winter and mid-spring, and again between mid-summer and mid-autumn. If we think of the circle as a unit circle with the pi/2 position being full tilt toward the sun (summer solstice) and the shadow falling from 0 to pi (the x-axis), we see that the poles’ (and hence the hemispheres’) distance from the shadow line (the x-axis) is a sinous function of its movement along the circular path.

]]>I was just thinking about this today as we’re coming into the six weeks around the equinox where we’ll gain the most light all year…

I’m not clear on where the 79/21 comes in – I may not be visualizing this correctly. The way I have it drawn is a square inside the quarter circle between 0 and pi/2, with sides of length 1/sqrt2 and diagonal running from the center to pi/4 (also a radius) =1, which makes their ratio (sqrt2)+1. If you get a chance, let me know where I’m going wrong here.

Thanks for the input!

]]>