If you imagine a pyramid made of square blocks, which five blocks (units) high and has five blocks along its base (25 blocks). It isn't important that it be pointed at the top.
What is significant is that the distance from the point at the top, to the base is five units. If you like you can measure from the centre of the blocks.
The point is that the inverse square law works fine with two blocks if you are calculating (illumination) out two units from the top, (or to the base), and fine for five, but becomes complicated if you are calculating just one unit.
This is because we are using the language of mathematics to describe what we see. We cannot believe it unless we can express it mathematically, but unfortunately there is no nobel prize for mathematics.
Diag 3
Diag 5 Centre of a Helium nucleus.
Don't worry at this point about the pictures of crop circles. They are mostly man made, but we are just looking at them as geometric shapes with no meaning. If we recognise any shape in particular as representing the shape of a sub atomic structure it is probably a coincidence.
What we need to do is imagine two circles, one being four times the size of the other, the smaller inside the larger. A circle is a object in two dimensions, and a sphere is an object in three dimensions. In string theory there are up to 21 dimensions, but it is hard for us to imagine.
If we
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1.
The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.
Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value truncated to 65 decimal places is
- 1.4142135623 30950488016887 24209
- 6980 8569 7187 37694 807317667973799...
- (sequence A002193 in OEIS)
- The quick approximation 99/70 for the square root of two is frequently used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000.
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