Archive for July, 2006

Circles

Posted in Int. 1 Maths, SG Maths on July 3rd, 2006

Sometimes it’s quite difficult for people to get a handle on circles. Here’s a quick reminder of the main bits:

A circle
A circle is a line which is made up of all the points which are the same distance from the centre. The distance is called the radius (see below).

\reverse\opaque\picture(100){(50,50){\circle(100)}(50,50){\circle(3)}}
This circle is the line drawn 50 pixels distant from the centre.

A chord
A chord is a line in a circle which cuts the circle in two:

\reverse\opaque\picture(100){(50,50){\circle(100)}(0,60){\line(75,34)}}

The diameter
The diameter is a line in a circle which cuts the circle into two equal parts. The diameter is the longest chord:

\reverse\opaque\picture(100){(50,50){\circle(100)}(0,50){\line(100,0)}}

The cirumference
The cirumference is the length of the line which makes the circle. The circumference of a circle is its perimeter and it is always\reverse\opaque\pi=3.1416 times the diameter:

\reverse\opaque\picture(400,150){<br /> (50,100){\circle(100)}<br /> (0,100){\line(100,0)}<br /> (0,40){\line(314,0)}<br /> (0,38){\line(0,4)}<br /> (100,38){\line(0,4)}<br /> (200,38){\line(0,4)}<br /> (300,38){\line(0,4)}<br /> (314,38){\line(0,4)}<br /> }

That PI thing
The greeks discovered that there are always 3.1416 diameters in the circumference of a circle. So as to avoid having to say “that number what is the exact number of diameters in the circumference” all the time, they invented a kind of shorthand code for it. They could have called it \reverse\opaque{x} but they didn’t have a letter for it, so they used their letter p instead. The Greek letter p is \reverse\opaque\pi. You can either use the \reverse\opaque\pi button on your calculator to get it, or you can use an approximate value like 3.14, or 3, or \reverse\opaque\frac{22}{7}. If you want to know what \reverse\opaque\pi is to a million places, click here.

The radius
The radius is a line in a circle which starts at the middle and goes straight to the edge. It looks like the arm of a radar screen. A radius is half a diameter.

\reverse\opaque\picture(100){(50,50){\circle(100)}(50,50){\line(35,35)}}

The area of a circle
The area of a circle is found by multiplying the radius by itself, then multiplying by \reverse\opaque\pi.

\reverse\opaque{A}=\pi\times{r}\times{r} = \pi{r^2}

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