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.

Other Research Papers about Masonic History and Symbolism written by Bro.William S.Burkle
¨ THE GEOMETRIC PROPERTIES OF TWO FIGURES ILLUSTRATING THE PROPORTIONS OF THE BODY OF MAN BY H. C. AGRIPPA This paper explores two classic examples of symbolic illustrations which appear in Book Two, Chapter xxvii of Three Books of Occult Philosophy , by the noted 16th Century Alchemist, Henry Cornelius Agrippa, entitled “Of the Proportion, Measure, and Harmony of Man’s Body”. These symbols are very complex geometric figures accompanied by obscure references to philosophical concepts. The exploration undertaken in this paper will specifically focus upon the geometric properties of the figures.
¨ 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.
¨ INTERESTING PROPERTIES OF THREE MUTUALLY TANGENT CIRCLES WITH CENTERS AT THE VERTICES OF 3,4,5, RIGHT TRIANGLE Constructing three mutually tangent circles at the vertices of a 3, 4, 5 Right Triangle produces some interesting results. This paper explores how tangent circle triads arranged to produce a well-known Pythagorean (Euclidian) triangle may offer insight into the triangles mystic properties.
¨ 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.
¨ THE MASONIC LADDER AND THE GREAT CHAIN OF BEING This paper examines the esoteric symbolism of the Masonic Ladder and will develop the thesis that the Masonic Ladder'??s esoteric meaning derives from an ancient concept dealing with the hierarchal ordering of the universe known as the Great Chain of Being . This ordering was so ingrained in the cultural, political, and theological structure of society that it was accepted as a matter of absolute fact at least until the late 1800'??s or early 1900'??s. This paper will discuss the concept of the Great Chain of Being, will examine its historical basis, and will explain how the esoteric symbolism of the Masonic ladder is related to this concept.
¨ A GUIDE FOR THE NEW ESOTERIC FREEMASON This paper presents a viewpoint which supports that esotericism is a legitimate element of the Craft and exists by design, and that Freemasonry is the inheritor of a great wealth of secret knowledge which has been encoded in our rituals, symbols, and traditions. It argues that many Blue Lodges are not equipped to Mentor the new Mason who expresses esoteric interests in the Craft. This paper also presents a description of what constitutes Esoteric Masonic practice, identifies reading materials (a topical list) for esoteric study, and provides a suggested curriculum (linked to the topical reading lists)which provides the new Esoteric Mason with a thorough course of study.
¨ ESOTERICISM OF THE GAME OF CHESS RELATED TO FREEMASONRY by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. This paper examines the esoteric properties of the Chess Board and the Chess Pieces, identifies the underlying spiritual meanings of the game and reveals the close ties between Chess and esoteric Freemasonry.
¨ THE KNOTTED ROPE IN MASONIC ESOTERIC TRADITION by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. The knotted rope is an ancient Masonic Symbol commonly associated with the Tessellated Border. The Author examines the esoteric characteristics and uses of the knotted rope both in non-Masonic traditions as well as in Masonic tradition.
¨ THE TETRAGRAMMATON, THE PENTAGRAMMATON, AND THE ADAM KADMON: A FUSION OF CHRISTIAN AND HEBREW MYSTICISM by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. During the early 17th Century, there was a resurgence of popular interest in Christian Mysticism in the form of Rosicrucianism. Rosicrucianism presented Mysticism in allegorical form, applying a mixture of esoteric traditions and symbolism from disparate cultures to achieve a new contextual understanding of Christianity. The tenets of the Hebrew Kabala, were of particular importance in the formulation of Rosicrucian doctrine, and were seamlessly integrated with Christian Mysticism as a part of the Rosicrucian belief system. One of the more interesting fusions of Hebrew and Christian Mysticism involved the extension of the Tetragrammaton, the ineffable name of G_d, into the Pentagrammatron, the Hebrew characters used to represent the name of Jesus. By further extension, this fusion came to include the transformation of the Adam Kadmon symbolically portrayed using the four Hebrew characters of the Tetragrammaton into the Adam Kadmon, formed using the five characters of the Pentagrammaton.
¨ MEMENTO MORI - THE SYMBOL OF THE SKULL WITH CROSSED BONES A Perspective on Death and Dying in the Chivalric Orders of the York Rite of Freemasonry by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. The symbol of the Skull and Crossbones, often called the Memento Mori, is a grim reminder of our own mortality. This paper explores the history of the Momento Mori as artwork, as Christian symbolism, and in the context of it's use in the Christian Chivalric Orders of the York Rite of Freemasonry.
¨ THE SEPHIROTH AND THE FOUR WORLDS IN THE THREE DIMENSIONAL PERSPECTIVE by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. The concept of the Sephiroth and the Four Worlds is a difficult to understand, but essential, part of Freemasonry. This paper examines features of a Three-Dimensional model of the Sephiroth proposed by Robert Wang, secretary and protege of Israel Regardie of Golden Dawn fame. Wang's three 3-d model portrayes the four worlds with the geometry of the Sephiroth represented as a double cube with a center column as the Pillar of Beauty.
¨ TWO ESOTERIC MASONIC CONCEPTS WHICH ARE LINKED BY THE TETRAGRAMMATON by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. The Tetractys and the Sephiroth represent similar concepts; however the link between these two concepts would not be readily apparent were it not for their common use of the Tetragrammaton. The Tetagrammaton serves as a bridge between these concepts which span time, culture (Greek and Hebrew), and multiple Masonic rites and rituals. This paper discusses the Tetragrammaton, the Tetractys, and the Sephiroth and shows how the three are related.
¨ THE BROKEN COLUMN AND ITS DEEPER MEANING by Bro. William Steve Burkle KT, 32°, Scioto Lodge No. 6, Chillicothe, G.L. of F.&A.M. of Ohio. discussion of the evolution of the Three Great Columns from Plato's (Cardinal) virtues and the Sephiroth. It then examines the Broken Column as one of the Three Great columns. This paper establishes the allusion of Solomon to the column of wisdom, Hiram King of Tyre to the column of strength, and Hiram Abif to the Broken Column (Beauty).
¨ THE MAJOR ARCANA OF THE TAROT AND FREEMASONRY Masonic Allusion and Symbolism in the Figures and Interpretations of the Major Arcana of the Tarot by Arthur Edward Waite
¨ NINETEEN FREEMASONS AND THE OCCULT REVIVAL OF THE LATE 19TH CENTURY This paper explores the role of nineteen regular Freemasons in the occult revival of the late 19th and early 20th centuries, and discusses the occult beliefs and organizational roles of these Freemasons during this period.