I'm currently studying the trigonometry behind biorhythms. I was reading through the Wikipedia article on the topic (https://en.wikipedia.org/wiki/Biorhythm) which states that:
Basic arithmetic shows that the combination of the simpler 23- and 28-day cycles repeats every 644 days (or 1-3/4 years), while the triple combination of 23-, 28-, and 33-day cycles repeats every 21,252 days (or 58.18+ years).
From my understanding, these are instances where they intersect on the x axis, but I may be mistaken.
What I am looking for are the points in time when two and three of the sine waves intersect and do so exactly when intercepting the x axis (x, 0). These are refered to as "double critical" and "super critical" days respectively. I have read articles and watched videos explaining how to find intercepts of sine waves, but I am unable to find an explaination as to how this can be used when a particular coordinate is wanting to be found.
The equations for the three waves are as follows:
- Physical: $\sin(2πx/23)$
- Emotional: $\sin(2πx/28)$
- Intellectual: $\sin(2πx/33)$
All the waves start at the point (0,0) at the date of birth. For consistancy, let's make that 1/1/1970.
Would someone be able to explain the process required to solve this?
Thank you in advance,
Lachlan
To determine how many days it takes for the cycle to repeat itself, multiply the different cycles by themselves.
For example:
23 × 28 = 644 days
Finding the intersection point requires finding the LCM of each combination.