Freemasonry and Geometry

William Stephen (Steve) Burkle
Masonic Memberships and Affiliations:
Bro.William Stephen Burkle, Master Mason is member of:
Scioto Lodge No. 6, F. & A.M., Chillicothe, Ohio
(Candidate), Philo Lodge No. 243 F. & A.M., South River, New Jersey
5th Capitular District, Chillicothe Chapter No. 4, R.A.M., Chillicothe, Ohio
6th Arch, Chillicothe Council No. 4, R. & S.M., Chillicothe, Ohio
4th Division, Chillicothe Commandery No. 8, K.T., Chillicothe, Ohio
Valley of Columbus, A.A.S.R., Dublin Ohio; Council, Chapter, Consistory
Aladdin Shrine, A.A.O.N.M.S., Columbus, Ohio
Bro. Steve is also member of The Philalethes Society and The Scottish Rite Research Society.
He is webmaster of Scioto Lodge No. 6 A. & F.M. - http://www.sciotolodge.com.

¨ SPECULATION ON THE SYMBOL OF THE SQUARE AND COMPASSES - Freemasons’ Magic Square

This paper is an the exploration of our Masonic tradition, and the resulting discovery of what is either a startling coincidence, or true information hidden within one of our most cherished Masonic symbols.

¨ FURTHER SPECULATION ON THE SYMBOL OF THE SQUARE AND COMPASSES.
In which the author uses numerology, substitution cipher, and English gematria.

This paper presents that portion of my exploration of the Masonic Square and Compasses symbol dealing with the techniques of Numerology, English alphabet substitution cipher (using the Pythagorean Cipher Chart), and three variants of English Gematria.

¨ THE POINT WITHIN A CIRCLE - More Than Just an Allusion?

The figure representing this symbol contained not only a point within a circle, but also two straight vertical lines touching the sides of the circle. It was explained during the ensuing lecture that these lines represented the two Holy Saints John, namely John the Baptist, and John the Evangelist. This struck me as peculiar to say the least, and I have been trying to figure out this peculiarity ever since.

¨ EUCLID, THE POINT WITHIN A CIRCLE, THE VESICA PISCES AND DIVINE PROPORTION

The 47^th Proposition of Euclid and the Masonic symbol of “The Point Within A Circle” are important in the Craft as symbols of philosophical premise, and are fundamental in that capacity to an understanding of Freemasonry.

¨ DOES THE POINT WITHIN A CIRCLE ALLUDE TO THE AUTUMNAL EQUINOX ?

This paper describes a possible link between the traditional, metaphoric interpretation of this symbol and a complex ancient system for star mapping. This link in turn leads points to a connection between The Point Within A Circle, and an astronomical event known as the Autumnal Equinox.

¨ A PROOF OF EUCLID'S 47th PROPOSITION Using Circles Having the Proportions of 3, 5, and 7.

The numbers 3, 5, and 7 are significant in the Craft, as is evident from the dramatic manner in which these numbers are brought to the attention of a Fellowcraft Mason during the ritual of the Degree.

¨ A PROOF OF EUCLID'S 47th PROPOSITION
Using the Figure of "The Point Within a Circle" and With the Kind Assistance of President James A. Garfield.

There are various mathematical proofs of Euclid's 47^th Proposition. One of these proofs immediately caught my eye, since it had been developed by Brother James A. Garfield, the twentieth President of the United States, and a Freemason.

¨ THE 47TH PROBLEM OF EUCLID - THE VEIL LIFTED

The 47th Problem of Euclid is enigmatic; while it is ostensibly a proof of a key principle of Geometry, its esoteric characteristics, not its mathematical properties are the source of its Masonic significance.

¨ THE PYTHAGOREAN THEOREM. Is This Ancient Mathematical Equation Encoded in the Masonic Allegory of the Spiral Stairway?

It is the premise of this paper that the root method for the derivation of the numbers 3, 5, and 7 which are prominent in the description of a certain winding stairway, contains encoded within itself the Pythagorean Theorem. A mathematical proof of this premise is offered.

¨ MUSINGS ON THE GEOMETRIC PROPERTIES OF THE SQUARE AND COMPASSES

It is the premise of these articles that the Square and Compasses symbol neatly fits the three-by-three grid which comprises the Freemason’s Magic Square and that by using simple cryptographic techniques such as Alphabet/Number substitution (employing for example the Pythagorean Chart), some previously encrypted message may be revealed.

¨ PARADOX IN SCIENCE, LIFE AND FREEMASONRY

This paper deals with the paradox of Quantum phenomenon and the reflection of this paradox in literature, art, music, religion, and Freemasonry.

¨ THE SONG OF THE LABYRINTH

This paper undertakes an examination of the rhythmic properties of the Chartres Labyrinth and provides details of the analytical methods used for this examination.