# Some interesting pics

#### dwsmith

##### Well-known member
The Love Formula only generates the right half of the plot!

#### Klaas van Aarsen

##### MHB Seeker
Staff member
The Love Formula only generates the right half of the plot!
We do get a full heart. See W|A.

#### dwsmith

##### Well-known member
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

##### MHB Seeker
Staff member
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

##### Well-known member
MHB Math Helper
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

##### MHB Seeker
Staff member
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.