BIORHYTHMS ON THE TI-NSPIRE

Transcription

1 BIORHYTHMS ON THE TI-NSPIRE Biorhythm theory states that a person s biological functioning is controlled by three phenomena (emotional, physical, intellectual) that vary sinusoidally with time. It uses the graphs of three simple sine functions to make predictions about an individual s physical, emotional, and intellectual potential for a particular day. Note that some programs also have intuitional. A biorhythm relates to a particular month in a particular year and needs to be recalculated for each new month. The graphs are given by y = A sin(bx) where x = 0 corresponds to a person s date of birth and where A = 1 is used to denote 100% potential. The theory states that when the physical cycle is near a high point, the person can do well in physical activities, and so forth. A. The first part of this document uses the standard format f(x) = sin (x). The days of the designated month will be recorded based on days lived, B. The second part performs a translation in the form f(x) = sin(x-c). This is to allow the days of the month to be more meaningful. i.e. day 1 day 31. This requires some more conceptual understanding than Method A. As the cycles are dependent on birth date it is necessary to calculate the number of days you have lived at the start of the month being investigated. Using the Days between dates (dbd) function on your handheld When in the Calculator Application press k, scroll to dbd( and paste. Enter as dbd(ddmm.yy,ddmm.yy). i.e 1 st June 2008 would be entered as Use the above values to set the Window on your handheld if using Method A (i.e. non translated form) Assume birth date: 29th March, 1970 **dates must be between 1950 and Texas Instruments Australia 2008 Author: Russell Brown 1

2 Method A: If the physical cycle has a period of 23 days, then 2 π = 23. Solving, we find that B B = 2 π. The physical biorhythm can be described by the equation 23 2π physical( x) = sin( x). 23 If the emotional cycle has a period of 28 days, then B =, and the emotional biorhythm can be described by emotional(x) =. If the intellectual cycle has a period of 33 days, then B =, and the intellectual biorhythm can be described by intellectual(x) =. Define these as functions in the Calculator Application In the Graphs & Geometry Application paste in the function variables as defined above. Press h to get the list of stored variables. Press after each entry to sketch the function. Press b[window][window Settings] and set as determined below. The minimum X-value is equal to the number of days that you have lived from your birth to the first day of this month (June, 2008). For your information, were leap years. What! You need to go even lower than this?? XMin = To get the maximum X-value, add the number of days in this month (June) to the minimum X-value. XMax =.. ( XMin + 30) Note: to show the end values on a graph you need to select the axes, press /+b and select Attributes. Change the attribute shown opposite. Texas Instruments Australia 2008 Author: Russell Brown 2

3 Unfortunately it is a bit difficult to check specific days in this scale format. The following method sets up a translation to set a more appropriate scale structure. Method B: Whilst a little more understanding of circular functions is needed, this is a neater approach as well as addressing the concept of translation of functions. By applying a horizontal translation the Window can be set up to show Day 1.. day 30 (or that required for the specific month) Calculate dbd as shown earlier. As you want the 1 st of the month to show as 1 instead of in our example above you would need to translate to the left units. This can be done using variables as shown below or for an easier approach, just type in the new translated function as shown on the last line in the screen image below. Texas Instruments Australia 2008 Author: Russell Brown 3

4 Set the Graph Window to suit the month. i.e. in this example XMin = 1& XMax = 30. To see what an individual day brings, add a perpendicular to any tic mark on the x-axis (use b 91). By placing the perpendicular on a tic mark it will jump to the next mark when dragged. Find the equation using b16 and click on the perpendicular line. Grab the point on the axis (move cursor over point, a appears. Hold down the a button until the hand closes. Use cursor to jump between tic marks) Texas Instruments Australia 2008 Author: Russell Brown 4

5 This is what the experts say!!!! There are four known biorhythm cycles: physical, emotional, intellectual and intuitional (38 day cycle). Each of these cycles starts at the time of birth. From this point, each of the cycles starts to rise up through its active phase until it falls back to the zero level. Then it continues through the zero level to go on to a passive phase. Then it rises again to the zero level to begin all over again. Each time the cycle crosses the zero level from the active to the passive phase, it is said to be in a critical state (critical day). When the cycle crosses the zero level from the passive to active phase it is said to be in a zero state (zero day). In the active phase the abilities associated with the particular cycle are high. When the cycle is in its passive phase the abilities are diminished. During the critical day the associated abilities are unstable, and you should be really careful during that day. The 'zero day' can be various. The abilities are unstable during that day as well. However this day is better than a critical day because the cycle is heading towards the active phase. In practice we are under influence of the combination of all the cycles. Some questions What is your best physical day (s) for the month? What is your best emotional day (s)? When should I schedule a test in order for you to do your best? When should I schedule a test in order for the entire group to do their best collectively? What will be your best overall day during the month? Why? Biorhythm theory says that the most dangerous time, your critical day, for a particular function (accidents, illness, and bad decisions) is when it crosses the time axis on the way down! During the month plotted, what is the date when this first happened for your physical function? Emotional? Intellectual? When it crosses from negative to positive it is called a zero day. Is this as bad? On the day you were born, all three cycles are at zero. How often would you expect this to occur during your life? Texas Instruments Australia 2008 Author: Russell Brown 5