How to make animated calculations and graphics

Posted on lunes, junio 14, 2010 by Pedro Wave

Who said that computation is boring?
Hands up!

This question has arisen in many schools and it is time to answer it with foundation.

Since 2003 the schoolchilds of my village have in their desks Tablet PC donated by the computer magnate, they are the masters of the keyboard and the homework!

Who would have said in one of the areas in Spain that are becoming depopulated soon be our grandchildren who have the last and better resources. Now what remains is to give content to these PCs and, not only with the Bill Gates Windows, making them attractive to schoolboys and schollgirls, because what they hate most is monotony and do not like math because are a "real bore" but you can animate it a little.

But that is going to end if they are taught to do calculations that are not boring (before we had to learn to use the tables of logarithms and calculate cube roots by hand) and the best way is to present them graphically with the tools at our disposal, or either with "animate" Excel spreadsheets, what will be a more entertaining that the schoolchilds are close to the mathematical calculation, without neglecting the formulas and equations that make data come alive, do you like my waves?

What is important is that the teachers, in nursery, primary and secondary schools, approach to computers without fear, thinking about computers as allies instead of enemies, and receive support and computer classes in their curriculum, whether science as letters, because nowadays, who does not know how to use a computer is seen as an illiterate of XXI century can not be effective educators and their students either, as they are advanced users of new technologies, both for study and for work.

One way of bringing mathematics to the students is teaching them with computer programs and spreadsheets are a good ally because need equations to calculate, graphic spreadsheets and, why not, animate them!

How to make "animated" calculations and graphics in Excel?

Nothing better than an example, inventing the wheel again, or rather creating bubbles in the waves of this blog.

I'll use the circumference formula to calculate the coordinate points on the axes X and Y. Solving the unknown Y in relation to the radius R of the circle and the values of X, we obtain:

To do that, open a new Excel spreadsheet and write in the following cells:

Cell L6 - Radius R with number format without decimals.

Range K11:K211 - Integer values of x' consecutives from -100 to +100.

Range L11:L211 - Integer values of x being equal to R (with the sign of x if x ' > R) or equal to x', according to the formula:

Range M11:M211 - Value +y obtained from the formula for the circumference:

Range N11:N211 - Value -y changing +y sign:

Range O11:O211 - Random value between negative and positive values of y:

Columns P, Q and R as L, M and N but with a half circle of radius R / 2.

So far the calculations are based on the formula for the circumference of the column M. (If you want to know why ROUND is used to calculate the square root as explained in an article on Linear Equations here as it is a solution to the frequent calculation bugs)

To graph these two circles on a spreadsheet named "Waves" (Ondas in Spanish) follow these steps:

1) Insert a scatter graphic with straight lines.

2) Select data, adding 5 series: +y, -y, +y/2, y/2 and the series of random values (see steps 3 through 7)

3) Add the series +y for the positive values of the first circle:
Series name: 
Series X values: 
Series Y values: 

4) Add the series -y for the negative values of the first circle::
Series name:
Series X values:
Series Y values:

5) Add the series +y/2 for the positive values of the second circle:
Series name: 
Series X values: 
Series Y values: 

6) Add the series -y/2 for the negative values of the second circle:
Series name: 
Series X values: 
Series Y values: 

7) Add the series of random bubbles:
Series name: 
Series X values: 
Series Y values: 

We already have the graph to which you can remove all but the series, eliminating the axes, titles, gridlines, etc., only to see that the graphics are stopped by now.

To animate the graphics we need to create an Excel macro to be launched by a button that will start changing the radius R values to change the circles in real time, but I will explain in another article that this is already long enough.

As an aperitif, to modify the radius R you could add a scrollbar to the spreadsheet, following the instructions on this link (personally I like the form controls)

Download Pedro Waves

You can download the animated graphic from here: 

When you open it, you will find 2 files:
pedrowaves.xlsm for the Excel 2007 and 2010 versions (recommended!)
pedrowaves.xls for previous versions.

To view the animation you must enable macros and press Play.

Traducción al español aquí.

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