Friday, February 13, 2009

Graphing Hearts

A conversation of the TI-Nspire Google Group occurred today about graphing implicit functions. The expression entered for the graph to the left demonstrates another reason to "go CAS." With the TI-Nspire CAS you can easily graph implicit relations, especially conics. CAS has its advantages. (When using this 'zeros method', remember the ",y)" at the end.)

I was impressed with using the zeros feature to graph this. On my TI-Nspire Calculus website I have a file where hearts are graphed from functions with radicals and inverse trig functions. There are also 2 kinds of polar hearts, a parametric, and an implicit heart graph plotted using a different method than the lovely 'zeros method' shown on the left. I made a pdf of the heart graphs for the enjoyment of all.
(Update: See what graphing a heart in 3D looks like on the 3.0 operating system of the TI-Nspire CX. This works on the numeric or CAS Nspire.)

Romans 13:8 "Let no debt remain outstanding,
except the continuing debt to
love one another,
for he who loves his fellowman has fulfilled the law."


Anonymous said...

Mr. Bird,

As before, I find the notation confusing:

Is f1(x) the same as y???

Do you understand my confusion?

- Bill

Claire said...


Mr. Bird said...

Perhaps it would help if you saw the output of the zeros() function on a Calculator page. 1st off, zeros((x^2+y^2-1)^3-x^2*y^3,y) results in a list of the positive and negative solution of (x^2+y^2-1)^3-x^2*y^3=0
The TI-Nspire can graph a list of functions. For example, graph f1(x)={-1,1}sqrt(x)
To answer the question about is f1(x) the same as y, consider that with the TI-83/84 you would graph y1=, y2=, etc. Actually it was y1(x)= and y2(x)=, but you didn't really notice that unless you were on the home screen asking for y1(2), for example.

Anyway, the zeros(expression,var) solves an expression that is equal to zero for what ever variable you request. With the example of the heart, the equation (x^2+y^2-1)^3=x^2*y^3 is graphed by, yes, getting f1(x)=y.
The equation is solved for y with a little help from CAS.

Anonymous said...

Or use these 2 equations:

Ainatul Amin said...

I am very new with the calculator. How can i put the zeros there? Can i just type it?

Mr. Bird said...

Yes you just type zeros(expressions,variable). Use the y-variable.