My three year younger
brother, Noel, after studying my unproven observations
and make up of octagon
formulas now proves that my perceptions and formulas do have a basis in fact. (BIF)

Since Noel as a young
teenager designed and built functional radio receivers,
long distance radio transmitters and radio directional
antennas I've known that Noel was exceptionally
gifted and talented
in the fields of optics, electronics, mathematics and
original thinking.

In Noel's own words, here is
his proof of my, until now, unproven octagon formulas.

Noel
Reekie's Proof that the Side of a Regular Octagon
is Equal to 0.4142 Times the Width of the Octagon.

First prove that EF = BD

If AC and OC = 1

Then AO and AD = the
square root of 2

Therefore CD = the square
root of 2 minus 1

Similarly BC = the square
root of 2 minus 1

Since AE = 2

Then EF = 2 times the
square root of 2 minus 1

As does BD = 2 times the
square root of 2 minus 1

Therefore EF = BD

Now if AE = 1

Then EF = the square root
of 2 minus 1
= 0.4142

Since EF = BD

Then BD = 0.4142 times the
Width of the Octagon

Noel
Reekie's Simplified Proof that the length of the
Side of an Octagon is 0.4142 times the Width if the
Octagon.

AC = 1

AB = 0.5

BO =
0.5

Therefore AO = the square
root of 0.5 as does AE, OC and CD = 0.7071

BE = 0.7071 minus 0.5 = 0.2071

Similarly BD also = 0.2071

DE =
BE + BD
= 0.2071 + 0.2071 = 0.4142

Thanks Noel. Now I can
think about something else!