Algebra in parenthood
Can you remember the formulae for calculating the area and circumference of a circle from the radius? Working it backwards? Did you ever think at school "this is a waste of time"?
Well, it is vital you know how to do this when looking at playpens. I kid you not!
How many pies?We're looking at a couple of options for playpens, one of which is this one. The alternative one has the diameter listed, but this one doesn't, jut that each side is approx 61 cms. So how big is it?
Well, there are two mathematical approaches that can be taken. One involves meat pies, the other some guy called Pythagoras. We opted for the pies.
What's the circumference? 6 sides of 61 cms is 366cm. Now a hexagon is almost circular, so given that the circumference of our "circle" is 366 cm...
circumference = 2.π.r
366 = 2.π.r
366/2 = π.r
183/π = r
58.25 = r
So our radius is approx 58.25 cm, with our diameter being 116.5 cm.
Phewww...
OK, retired maths teachers, give us the Pythagoras route!
Comments
I sometimes despair! People with degrees can often miss the obvious and punching computer keys is no effective alternative to knowing your mathematics.
I believe the play pen is hexagonal (which you chose to inscribe in a circle - God knows why!)
A hexagon, for the uninitiated like people with degrees, consists of six EQULATERAL triangles.
Therefore if one side is 61 cms then the radius of your surrounding circle is also 61 cm. Hence the diameter (point to opposite point in your hexagon) is 122 cms.
Now, say hello to old Pythagoras and learn a little!
Let A be a point midway along one of the hexagon's sides.
Let B be the end of the side in question and let C be the centre of the inscribing circle.
In the triangle ABC we have one side measuring 30.5 cm (half of 61) and a hypotenuse of 61 (the radius of the superfluous circle).
Pythagoras he say: BC squared minus AB squared equals AC squared.
Forget your calculator - use a pen and paper and you'll find that AC squared equals 2790.75, the square root of which is 52.8275.
Double this and you should get 105.655 (which is the distance across the flats of your hexagonal play pen)!
Easy for us old codgers but too complicated for young pups with degrees.
Finally - a word of advice from this mathedmatical guru - don't opt for a playpen which is a heptagon or nonagon or similar!!
Posted by: Retired Euclidian | November 1, 2006 10:42 AM
Retired Euclidian,
In our days since leaving school we've been busy procreating, so we'd forgotten the hexagon was made of 6 equilateral triangles. It made sense (at the time) to equate the hexagon as a circle, as we are unsure exactly how the playpen will be positioned. It may rotate during installation by two or three degrees. The the distance across the flats is too small a gap, and it all goes horribly wrong.
Of course we'll heed the advice about going for pens of other polygonalistic nature, it's hard to find the cushions for them in John Lewis!
Posted by: Lee | November 1, 2006 5:00 PM