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#### masters

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- Jan 30, 2012

- 13

- Thread starter masters
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- Jan 30, 2012

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

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- Mar 5, 2012

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

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

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- #5

- Mar 5, 2012

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Note that $\sqrt[3]{x^2}$ is not the same as $x^{\frac 2 3}$.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.

With the latter, you'd only get half a heart (since it is not defined for negative numbers).

- Jan 17, 2013

- 1,667

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

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- #7

- Mar 5, 2012

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

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.