Some interesting pics

[masters]

 

[dwsmith]

View attachment 646View attachment 647View attachment 648View attachment 649View attachment 650

The Love Formula only generates the right half of the plot!

 

[Klaas van Aarsen]

The Love Formula only generates the right half of the plot!

We do get a full heart. See W|A.

 

[dwsmith]

We do get a full heart. See W|A.

Not on the actually version of Mathematica. I used implicit plot, contour plot, and regular plot with the plus and minus square root. Only half.

 

[Klaas van Aarsen]

Not on the actually version of Mathematica. I used implicit plot, contour plot, and regular plot with the plus and minus square root. Only half.

Note that $\sqrt[3]{x^2}$ is not the same as $x^{\frac 2 3}$.
With the latter, you'd only get half a heart (since it is not defined for negative numbers).

 

[ZaidAlyafey]

Note that $\sqrt[3]{x^2}$ is not the same as $x^{\frac 2 3}$.
With the latter, you'd only get half a heart (since it is not defined for negative numbers).

Do you mean that $ x^{\frac{2}{3}}$ is not defined for negative numbers ?

 

[Klaas van Aarsen]

Do you mean that $ x^{\frac{2}{3}}$ is not defined for negative numbers ?

There are different definitions for $x^{\frac{2}{3}}$.
Different choices for its domain can be made.
For instance $x^\alpha$ where alpha is a positive real number, is only defined for $x \ge 0$.

More to the point, calculators cannot calculate $(-1)^{0.6667}$ as a real number.
And they usually do not have exceptions for the special case where the power is a whole numbered fraction with an odd denominator, which is the only case where $x^\alpha$ can be defined for negative x.