Square Roots & Stuff

Square roots.  That sounds scary because there’s math involved.  Well don’t worry, this stuff’s easy.  Those scary numbers that look like √2, √3, and √5 are actually really simple concepts to understand.

√2 or “the square root of two” is simply the cross section of a square when the sides equal one.  The square root of five is the cross section of a double square.  And the square root of three is the number formed by the vesica piscis.

Square Root and Stuff

The square root of two is 1.414… because

1.414..  x  1.414.. = 2

1.732..  x  1.732.. = 3         So the square root of three is 1.732…

2.236..  x  2.236.. = 5       The square root of five is 2.236…

The square root of one is one because 1 x 1 = 1   The square root of four is two because 2 x 2 = 4

Now that you can connect these abstract numerical concepts to our geometrical reality they might make more sense.

Square Roots and the Golden Proportion

The Golden proportion (in gold) is found when we make a new circle (in blue) out of the vesica piscis.

Below are the square roots of one through five.

Square Origins
Many thanks to Sacred Geometry Decoded for inspiring me to make a few of these illustrations.

Square Roots and Golden Number

The square roots, seen yet another way.

Square roots Pi

√2 + √3 = π   This is 99.85% accurate according to the accepted value for π. Coincidence?

Egyptian Metrology

The ancients modeled their metrology based on the square roots.  One royal cubit is equal to one egyptian remen times the square root of two.

In his remarkable book City of Revelation (Ballantine Books 1972) the author John Michell points out the
geometric relationship between the Megalithic Yard, the Remen, and the Royal Cubit. If a square is drawn
with each side equal to one Remen, then the diagonal of the square is the hypotenuse of a right triangle and
is equal to one Royal Cubit (RC). If the base of the square is bisected and that point joined to the opposite
vertex of the right triangle, then the length of that line is equal to the radius of a circle with a diameter of one
Megalithic Yard (MY)

Ancient Measure    
Michell further points out that if an arc with radius equal 1 RC is scribed using the left hand corner of the base as centre and the process is repeated then a series of square root relationships is derived that corresponds to various ancient systems of measurement as follows:

Michell points out the following:

Magenta  = 1.2165 feet             = 1 Remen
Blue         = 1.2165 x root 2       = 1.72 feet = 1 Royal Cubit
Green      = 1.2165 x root 3       = 2.107 feet = 1 Palestinian Cubit
Yellow    = 1.2165 x root 4        = 2.433 feet = 1 Roman Pace
Red         = 1.2165 x root 5         = 2.72 feet = 1 Megalithic Yard

Earth’s diameter = 7920 miles
Moon’s diameter = 792 megalithic miles
Perimeter of the square containing the circle of the Earth = 31,680 miles
Perimeter of the square containing the circle of the Moon = 3,168 megalithic miles.
Sun’s diameter = 864,000 miles = 316,800 megalithic miles.  –Blog.World-Mysteries

Canonical Proportion joedubs

Although Michell goes on to point out many other relationships, this should be sufficient to show that the
English system of measurements has cosmological origins in common with other measurement systems in
the ancient world.  -Cosmic-MindReach.com

scott onstott square root phi
The illustrations above and below are by Scott Onstott – SecretsInPlainSight.com

square root Scott Onstott

The following is an illustration by Rich Jarvis  which shows the relationship between simple shapes and the square roots.  The radius of the circle is 1, or √1, same thing.  The diameter is 2 or √4.   A hexagon inside a circle has sides equal to the circle’s radius.  That is one of the special attributes of ‘six’, and perhaps why it is so highly revered.

rich jarvis square root

Looking at square roots in 2 and 3 dimensions

Square Root Geometry 5

The square root of three is found in the diagonal of a square when the length of the square equals one.

theory of thought

Origin of Square Roots by Theory of Thought

Golden Number - Earth and Moon

For my last trick, the square root of Phi is encoded in the Earth-Moon relationship.

√ø = 1.272019…  = the square root of Phi

Because 1.272 x 1.272 = 1.618… = Phi = The Golden Number

The Golden Number itself is based off of the square root of five.  Five and phi are inherently linked together and cannot operate independent of each other.

Square Roots for reference:

√1 = 1

√2 = 1.41421356237…

√3 = 1.73205080757…

√4 = 2

√5 = 2.2360679775…

√6 = 2.44948974278…

√7 = 2.64575131106…

√8 = 2.82842712475…

√9 = 3

√10 = 3.16227766017…

√11 = 3.31662479036…

√12 = 3.46410161514…

√13 = 3.60555127546…

 -√ø  ∑Dubs

√2 and the Yale Tablet

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I write about philosophy, geometry, health, politics and other stuff that interests me.


  1. Hi Joe
    I absolutely love your blog
    I can’t believe how many links you have that are a part of my own journey in the discovery of natural law
    I spent a lot of time with Jain here in Perth, Western Australia when he was here a year or so ago. He is a truly incredible person with an amazing mind and spirit
    Also I have been in contact with Richard Merrick of Interference theory 5 years ago
    Sonic Geometry is the closest media production I have found in unifying mathematics geometry music and base natural law in to an incredible unity
    I have been studying chaos for 16 years full time and the behaviour of crowd behaviour as viewed through the voting machine of the stock markets and currencies
    I commend you on your assembly of these incredible sets of coincidences
    Please keep them coming

    • Thank you, Chris.
      This blog has become a passion of mine. I’m glad others are enjoying the ‘cosmic coincidences’. Yes, I am a big fan of Jain’s work and hope to meet him one day. Interference Theory is also great stuff. Be sure to let me know if you are ever in Colorado – [email protected]

  2. Pingback: The Eye of wRAth & Pharisaic Mysteries of Sixty-three Serpents

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