Two dimensional things don’t exist. Everything has three-Dimensions!
The Sunday Nation
Nairobi,
08 September 2013
Peter Oloo says he was not convinced that two dimensional things do not exist. He writes: “You said that circles and triangles do not exist. What if I draw you a circle? Isn’t that a two dimensional object?”
No, Peter. It is not. If you were able to extract it from the piece of paper on which it is drawn, you’d be left with a very thing ring. We can even calculate its thickness. To do that, we need some basic information.
Assuming that you will draw it using a biro, we need to find out the amount of ink in the pen. The ink tube measures about 2mm in diameter and if filled to about 10cm. The volume is simply the cross-sectional area multiplied by the length.
The area is pi-r-squared; that is, 1mm (half the diameter) squared multiplied by 3.14. This yields 3.14 square millimetres. Before multiplying this by the 10cm length, it is important to convert everything to the same units of measurement. Otherwise we find ourselves mixing up oranges with lemons. Thus the 10cm goes into our calculation as 100mm – remember 10mm make 1cm.
Thus the volume of ink in the biro is 314 cubic millimetres. Cubic millimetres are also called millilitres; “ml” or “mills”. So, this is 314ml.
To find the thickness of anything written by the biro, we need to know two things: first, the length of the continuous line that can be drawn by the pen and second, the width of this line.
Most ordinary biros can draw a 1.5km line. If you feel up to the task, you can test whether this is true! Interestingly, not many people have ever used a biro from start to finish. The pens either get lost or stolen before the all ink is used up…
Any way, the width of the biro line is about 0.75mm, so, the question to answer is this: what would be the thickness of a 1.5km “block” that is 0.75mmwide and occupies 314ml of volume?
Again the volume is equal to the area (of the top surface, in this case) multiplied by the thickness. Thus the thickness is the volume divided by the area… that doesn’t look very complicated when written as a formula, thus: V = A x T; therefore T = V/A.
The area we are talking about here is 1.5km multiplied by 0.75mm. But, like before, we must work in same units; thus this is, 1,500,000mm x 0.75mm = 112,500sq.mm (remember, 1km = 1,000m and 1m = 1,000mm).
Now the last step: diving 314ml by 112,500sq.mm should give us the thickness of the line. This comes to 0.00279mm. In another “language” this is called 2.79micrometres, or simply 2.79 microns.
Now that’s quite thin. Compare it to the thickness of a piece of paper at about 100 microns. Nevertheless it is a measurable thickness and therefore any shape drawn with the pen is a three dimensional object – not two dimensions!
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