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Let's illustrate what we mean with a couple of examples. For the first example, we will consider the circumference of a circle. Hopefully, you know that thecircumference of a circle is given by the expression:
C = 2 * PI * r
where:
From this expression, we can conclude that
C $ r
If we modify the radius...
If we double the radius, the circumference will also double. If we reduce the radius by 25-percent, the circumference will also be reduced by 25-percent. Thisis illustrated by the script in Listing 2 .
| Listing 2 . Circumference is proportional to radius. |
|---|
<!-- File JavaScript02.html --><html><body><script language="JavaScript1.3">var r = 10
var C = 2 * Math.PI * rdocument.write("r =" + r +
", C = " + C + "<br/>")
//Multiply r by 2. Then display r and Cr = r * 2
C = 2 * Math.PI * rdocument.write("r =" + r +
", C = " + C + "<br/>")//Reduce r by 25%, Then display r and C
r = r * (1 - 25/100)C = 2 * Math.PI * r
document.write("r =" + r +", C = " + C + "<br/>")</script></body></html> |
Output from the script
When you open the script shown in Listing 2 in your browser, the text shown in Figure 2 should appear in your browser window.
| Figure 2 . Screen output for Listing #2. |
|---|
r =10, C = 62.83185307179586
r =20, C = 125.66370614359172r =15, C = 94.24777960769379 |
Figure 2 shows the value of the circumference for three different values for the radius. You should be able to confirm that the combination of thethree lines of output text satisfy the proportionality rules stated earlier .
For example, you can confirm these results by entering the following three expressions in the Google search box and recording the results that appearimmediately below the search box:
2*pi*10
2*pi*20
2*pi*15
Area of a circle
Before I can discuss the area of a circle, I need to define a symbol that we can use toindicate exponentiation.
A symbol for exponentiation
Physics textbooks typically use a superscript character to indicate that a value is raised to a power, such as the radius of a circle squared.
When I need to indicate that a value is raised to a power, I will use the "^" character, such as in the following text that indicates radius squared,or radius raised to the second power.
radius^2
In those cases where the exponent is a fraction, or is negative, I will surround it with parentheses, such as in
radius^(1/2), and
distance^(-2)
The first term indicates the square root of the radius. The second term indicates that distance is being raised to the -2 power.
I chose to use the "^" character to indicate exponentiation because it is used as the exponentiation operator in some programming languages, such asBASIC. The "^" character is also recognized by the Google calculator as an exponentiation operator.
Unfortunately, there is no exponentiation operator in JavaScript, so we will need a different approach to raise a value to a power in ourJavaScript scripts. As you will see later, we will use the built-in Math.pow method for that purpose.
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