There are a few approaches that I take to making these posts. Some data I will use from an online source (and reference), whereas others I will generate using equations. Since privately tutoring some local young people, I have had the pleasure (actually not sarcasm) of revisiting geometry. This meant that I had to relearn some basics – tan, cos, sin, etc. It took me back through my Sound Design degree days, but just in a different way.

Whilst tutoring, it was clicking how these functions can mimic stock market trends and how we can manipulate mathematical functions to accurately assess data plots. From an algebra perspective, I think of things like the Taylor Series (approximation), Laurent Series, or the Puiseux series. For all of the following functions, I will have an idea of how I would like them to look, but will finesse them using the Google Grapher function, i.e., Google: y=x^2+1 graph

https://docs.google.com/spreadsheets/d/1-GJlIK4TnF6BrDNibT84hqydsHDPFdI3M0HrvcYXNfM/edit#gid=0

Function 1

2.3*(sin(x)^2)+((x)^2)+5*3.14*cos(x-1)

=2.3*(SIN(I4)^2)+((I4)^2)+5*(3.14)*COS(I4–1)

Overall, I wanted a portion of a parabolic curve, but I wanted some variability within that curve over time. So, I integrate a collection of sine, cosine, and positive-degree polynomials to create the effect. This also makes it easier if I want to manipulate the function up/down (along the y-axis) or positive/negative (along the x-axis).

Link to Google Graph.

Function 2

-1.1*(sin(x)^3)+((x)^6)+2*(3.14)*cos(4*x-3)

=-1.1*(SIN(I4)^3)+((I4)^6)+2*(3.14)*COS(4*I4–3)

This is similar to function 1, but I wanted to create a downward sloping curve, based around costs and how they might change over time, especially unit costs. Using a combination of the sine, cosine, and odd-degree polynomial allows, again, for these interesting cost curve shapes.

Link to Google Graph.

Function 3

sin(x)*(1/cos(x)^3)*sqrt(x)+1/(x^n)

With the following set of conditions:

• If this equation is greater than 50, then reduce down to -1,
• If this equation is less than 50, then bump up to 1,
• Otherwise, return the equation.

=IF(

SIN(N4)*(1/COS(N4)^3)*SQRT(N4)+1/(N4^M4)>50, –1,

IF(SIN(N4)*(1/COS(N4)^3)*SQRT(N4)+1/(N4^M4)<-50, 1,

SIN(N4)*(1/COS(N4)^3)*SQRT(N4)+1/(N4^M4)

)

)

I have set these floors and ceilings to reduce the output range of the function, removing unbelievable outlier scenarios and to introduce believable seasonality. Instead of producing negative quantities, I would shift this curve up, making sure that it doesn’t cross the x-axis. However, I could also use this as a marginal cost curve, and use an integral to map a cost or demand curve.

Link to Google Graph.

This was a short post, but hopefully it helps to generate some ideas for you. Do you use your own functions to create data? Have you never thought about it before? Give it a go and post it in the comments! I would love to see what you come up with.