BIORHYTHMS

According to German physician Wilhelm Fleiss, there is a mathematical relationship between one's date of birth and one's behaviors throughout their lives. This is called a "biorhythm".

To calculate one's biorhythm, you must create periodic equations and model them through sine and cosine waves. The following are the calculations I made to find my own personal biorhythm.

To begin, I started with some basic information:
- My birthday is July 24th, 1998.
- I was born on the 205th day of the year.

I also did some research on "leap year", since this is a project dealing with measurement of time, which depends on whether or not that extra day is included.

Leap years exist due to the fact that we do not rotate around the sun in exactly 365 days. We rotate around the sun about 365.242374 days (according to the vernal equinox year). To try to make up for this, we add a day every four years, making up some of that time to keep astronomical events calculated for the same date at the same time every year.

However, since .242374 x 4 = .969496, we have not correctly measured the time we have tried to make up. There is about .04 of a day that we have added, which had pushed our calendar slightly forward in relation to astronomical events. For example, in about 100 years, we will have added an entire full day to the calendar, and events will be measured a day earlier than they actually occurred in accordance to the rotation of the sun.

Going back to the equations, the variables necessary, A, B, C, and D, all represent specific amounts dependent on this situation.

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• A = The scale relating to how good/bad your day is
• B = The amount of days alloted to the specific cycle
• C = Which day of the year you were born on
• D = How positive or negative you want your scale to be

Sine and cosine are also important parts of the equations. Sine and cosine are the best ways of modeling biorhythms since they show cycles. They show high points and low points and can be easily contrasted with other cycle models, as will be required here…

Using sine and/or cosine to model these equations could potentially make the C value smaller, since the numbers of days in each cycle are much lower than the number of days it takes to get to my birthday. It's much easier to use the smaller numbers, which can be modeled through variations of sine and cosine models.

Since the parameters for values A and D are independent and are only there for interpretation of the subject in question, I chose simple values to make the equations easier to understand. For value A, I chose 10, since it is an easy number to plot and decipher, and for D, I chose not to have any value at all, since I have about an equal number of good and bad days.

The value of B in each equation is relative to which cycle it is modeling, so the value of B for the physical model is 23, 28 for the emotional, and 33 for the intellectual.

Simplistically, the C value would be 204 since that is the number of days since January 1st. However, the smallest value possible is not 204, as previously introduced with the variations in sine and cosine equations.

After calculating the calculating the numbers through observation on desmos, I found that, through using both sine and negative cosine, I could achieve some very low C values and still model the same equation. The physical cycle gave me a value of 2, the emotional cycle -2, and the intellectual cycle 1.25.

After having found all of the values of the variables, it is then possible to piece together the equations:

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• f(x)=10sin(2pi/23(x+2))
• f(g)=-10cos(pi/14(g-2))
• f(h)=-10cos(2pi/33(h+1.25))

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If these equations were to be modified to model my biorhythms for January 14, 2015, my rating would be pretty average physically and intellectually, but very bad emotionally, as modeled in the following graph:

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In modeling my biorhythms for this month (October 2014), the first high points hit in each of these cycles are shown in the graphs as being:

PHYSICAL: about 12 days

EMOTIONAL: 20 days

INTELLECT: about 2 days

If I were to use this to find strategic points where I would be at my best this semester, I would change my C value from what I had in my October models and subtract 30. This would bring me to the beginning of September and I can observe what point(s) would render me at my greatest.