Advanced Math Honors



Mrs. Volynskaya Pre-Calculus Biorhythm Project Name___________

Background Information

The idea behind biorhythms is that our lives are affected by three cycles: physical, emotional, and intellectual. According to a theory called biorhythms, everyone has three inner rhythms that start at birth: a 23 day physical cycle, a 28 day emotional cycle, and a 33 day intellectual cycle. Each cycle consists of a high period, a low period, and a critical transition day when a person moves from one period to the other. These three cycles can be graphed so that a person can determine in advance when “good” and “bad” days will occur. The graph of each biorhythm cycle is sinusoidal.

These cycles start at a middle point when we are born and then fluctuate up and down throughout our lives. These biorhythms follow a sine wave with different periods. The physical cycle has a period of 23 days and affects strength, stamina, immunity to disease, coordination, and resistance to pain. The emotional cycle has a period of 28 days and affects mental stability, sensitivity, and moods. The intellectual cycle has a period of 33 days and affects the ability to learn, memory, analytical thinking, logic, and decision-making.

Below is a typical biorhythm chart for the month of March. The three sine graphs representing the physical, emotional, and intellectual cycles, have different periods (23, 28, and 33 days respectively.) 0 < x < 31 Emotional: line graph Physical: thick line graph Intellectual: dotted line graph.

To determine your biorhythm chart, first you must calculate the total number of days you have lived.

At the time of birth, the cycles start at a middle point known as the zero day. From this point, each cycle rises through the active phase and then back through the zero level to a passive phase. When the cycle passes from the active phase to the passive phase, this is known as the critical day.

To determine your biorhythm chart, first you must calculate the total number of days you have lived.

Don’t forget leap year.) Then you must divide the number of days by the period of each of the three

cycles and compute the remainder. That remainder will determine where you would begin each cycle.

For example, if the remainder when you divide by 23 is 9, then you are on the 9th day of your physical

cycle. Another way of thinking about this is to say that if you consider today as t = 0, then your sinusoid

had a horizontal shift of –9.

Finding Your Biorhythms

1. Give your birthday (include the year). Calculate the number of days old you are as of January, 2015. Remember, leap years occur on years that are divisible by 4 (e.g.: 1996, 2000, 2004, 2009…). If you use you MUST print out the results page.

2. Calculate the Period and Phase Shift for the physical, emotional and intellectual cycles. We want January 10, 2015 at the origin. **Hint: The cycle has been shifted back the number of days you have been alive.**

3. Write the equation of each function in the form Y = Asin(bx+c). Let the amplitude A = 100, so our cycle will cycle between –100 and 100. You might choose to use greater amplitude for those attributes that you deem more important. You might also choose to keep all your amplitudes the same. It is up to you.

4. Using the graphing online calculator ( ), graph each cycle for February 2015 and June 2015. Be sure to set our Ymin and Ymax to –100 and 100.

5. Put all 3 graphs together on one final sheet (different color for each graph & clearly label).

6. Write a few sentences about your emotional, physical, and intellectual outlook for the February and June 2015

Are there any particularly “good days” or “bad days” ahead? Explain.

7. Consider the graph of the sum of the three equations. What should it represent?

Grading (100 points total)

1. Birthdate; how many days old you are; show work ______/5

or print out the page from internet

2. Equations for each cycle with explanation and/or

work for each constant: b, and c for each Biorhythm:

Emotional ______/5

Intellectual ______/5

Physical ______/5

3. Rough sketches of each of the 3 equations

(Jan – June); 3 separate graphs; label axes

Axes Labeled for each graph ______/5

Graph of Emotional ______/5

Graph of Intellectual ______/5

Graph of Physical ______/5

4. One final graph (3 sine curves on one graph); ______/5

different color for each graph; ______/5

label graphs and axes clearly. ______/5

Identify critical days ______/5

5. Writing a few paragraphs about your emotional, physical, and intellectual outlook for the February and June 2015 ______/30

6. Conclusions – reflect on your work – what did you learned?

_______/10

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