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Is there a formula that will allow me to calculate the radius of a circle based on an input value? The input value could be as small as zero or as large as $10^7$, or larger. The circle is restricted to a minimum radius of $10$ and a maximum radius of $100$.

Does anyone know how to calculate something like this?

UPDATE

The input values correspond to state/country population. I want to calculate the radius (how big the circle should be) of the circle based on the input value.

Zachary Hunt
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  • What does the input correspond to? – Maazul May 21 '13 at 03:23
  • What is the input value supposed to be? If it is the radius of the circle, it is easy. Just raise everything below $10$ to $10$, and lower everything above $100$ to $100$. Explaining why this is not acceptable may help you define the problem better. – Ross Millikan May 21 '13 at 03:25
  • I made an edit, hope it helps. Thanks for the feedback. – Zachary Hunt May 21 '13 at 03:37
  • The update would have been useful in the original post. – Ross Millikan May 21 '13 at 03:39
  • Is this supposed to mean that on an input of say $200, 300$ and $400$, we ascribe the radius $10$ to $200$, $55$ to $300$ and $100$ to $400$? – Maazul May 21 '13 at 03:42
  • Yes. The smallest input value would have the smallest radius, and the largest input value would have the largest radius. Each value in between would have a different radius. – Zachary Hunt May 21 '13 at 03:46

3 Answers3

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For this application, I would just make the area of the circle proportional to the population. Let $R=\sqrt{\text{maximum population of a state/city}}$ Then plot each circle as $r=100\sqrt{\frac {\text{population}}R}$, boosting the ones you want to show that are below $r=10$ to $r=10$ to satisfy your minimum. But I don't understand the minimum.

Ross Millikan
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  • This is an important point - whatever the scaling factor, for visualization it's important to have area (and not radius) proportional to population. – Steven Stadnicki May 21 '13 at 05:01
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I'll expand on what I understood from your comment.

Let $\{x_i\}$ be the set of inputs.

Then the range of inputs is given by $\max\{x_i\}-\min\{x_i\}$.

The radius for the $i$th input is then given by

$$R=10+90\left(\frac{x_i-\min\{x_i\}}{\max\{x_i\}-\min\{x_i\}}\right)$$

Maazul
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$$r=10+\frac { 90 }{ { 10 }^{ 7 } } P$$ where P is your input and r is the radius of the circle.

newzad
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  • Just to be sure, does 10 represent the minimum radius? What does 90 represent? I assume 10^7 represents the maximum value in the ranse of possible values? – Zachary Hunt May 21 '13 at 05:04
  • $10$ is minimum radius,$90 = (100-10)$ = (maximum radius-minimum radius), $10^7-0 = 10^7$ population interval. In this case minimum population is zero so you can jsut write $10^7$$ – newzad May 21 '13 at 05:07