The Masonic Aprons - Geometrical Foundations Patrick G. Bailey, VIII Degree * Golden State College S.R.I.C.F. Los Altos, California August 23, 2015

Similar documents
Grade 8 Chapter 7: Rational and Irrational Numbers

Problem Set 3 (Individual) Due 2/16/11, 9:30am

Grades 7 & 8, Math Circles 17/18/19 October, Angles & Circles

H. Meij, H.P. Tokyo Chapter #1 R.A.M. February, 2000

Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)

The Shunammite Woman s Land Restored 2 Kings 8:1-6

MITOCW ocw-18_02-f07-lec02_220k

7 th Grade Algebra & Geometry Main Lesson Lesson Plan Outline

from Euclid to Einstein

A strangely synimetric pattern involving conjugacies and "local" and "global" bisectors

3.4 Pascal s Pride. A Solidify Understanding Task

SUMMER MATH PACKET. Geometry A COURSE 227

Introductory Quantum Chemistry Prof. K. L. Sebastian Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore

Numbers. The aim of this lesson is to enable you to: describe and use the number system. use positive and negative numbers

Dave wrote to his 3 rd Grade teacher From: Dave Date: (month/date/year, time) Subject: Greeting from Egypt To: Mr./Mrs.

Vectors. A vector is usually denoted in bold, like vector a, or sometimes it is denoted a, or many other deviations exist in various text books.

Take It To The Limit. Calculus H Mr. Russo Reaction to Take It To The Limit

{ }. The dots mean they continue in that pattern to both

Note: Please use the actual date you accessed this material in your citation.

Problem Solving. Kurt Bryan. Here s an amusing little problem I came across one day last summer.

MIT BLOSSOMS INITIATIVE

Antennas Prof. Girish Kumar Department of Electrical Engineering Indian Institute of Technology, Bombay. Module 02 Lecture 08 Dipole Antennas-I

LECTURE 16: Friction

Geometry Review- Chapter Find e, and express your answer in simplest radical form.

Take the Anxiety Out of Word Problems

Physics E-1ax, Fall 2014 Experiment 3. Experiment 3: Force. 2. Find your center of mass by balancing yourself on two force plates.

2. FUNCTIONS AND ALGEBRA

Looking Ahead to Chapter 10

How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots

Direct Proofs. the product of two consecutive integers plus the larger of the two integers

The Golden Ratio in Art and Architecture: A Critical Review. As a mathematician, I experience a thrill in finding connections between mathematics

MITOCW ocw f99-lec30_300k

1998 Harvard/MIT Math Tournament GEOMETRY Answer Sheet

Figure 1. Distance depends upon time.

Q25: Record the wavelength of each colored line according to the scale given.

Measurement: Length, Area and Volume Part I

Preparing Your Magical Equipment

AP Physics 1 Summer Assignment 2016

MITOCW 6. Standing Waves Part I

A page from Willow s computer diary

Vectors. A Vector is a quantity that has both magnitude and direction

PHY2048 Physics with Calculus I

2. l = 7 ft w = 4 ft h = 2.8 ft V = Find the Area of a trapezoid when the bases and height are given. Formula is A = B = 21 b = 11 h = 3 A=

Creating and Exploring Circles

Park School Mathematics Curriculum Book 3, Lesson 3: Trig and Shapes

Electromagnetic Theory Prof. D. K. Ghosh Department of Physics Indian Institute of Technology, Bombay

In this unit we will study exponents, mathematical operations on polynomials, and factoring.

Meridian Circle through Zenith, North Celestial Pole, Zenith Direction Straight Up from Observer. South Celestial Pole

College Physics 201 Graphing Review and Analysis

As the World Turns. Vocabulary rotate, revolve, tilt, frame of reference, spin, axis. Science Enhanced Scope and Sequence Grade 3

CHAPTER 1. Introduction

Assignment #0 Using Stellarium

AB Calculus: Rates of Change and Tangent Lines

Physics 6A Lab Experiment 6

Assignment 1 and 2: Complete practice worksheet: Simplifying Radicals and check your answers

Triangles and Vectors

Where Is Newton Taking Us? And How Fast?

CONTENTS NUMBER SYSTEMS. Number Systems

Don t forget to think of a matrix as a map (a.k.a. A Linear Algebra Primer)

STB-FE26 - Lesser Lights.TXT

6.1 George W. Ferris Day Off

Chapter 19 Sir Migo Mendoza

The Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as

A π day celebration! Everyone s favorite geometric constant!

P1-763.PDF Why Proofs?

Math (P)Review Part I:

STRATEGIES OF PROBLEM SOLVING

People. The Shadow Shadow People. The Shadow People A Reading A Z Level O Leveled Book Word Count: 874 LEVELED BOOK O.

Ex. 2: La)tude, Longitude, Spherical Distance

3.4 Pascal s Pride. A Solidify Understanding Task

A Quick Algebra Review

Chemical Applications of Symmetry and Group Theory Prof. Manabendra Chandra Department of Chemistry Indian Institute of Technology, Kanpur

HAMPSHIRE COLLEGE: YOU CAN T GET THERE FROM HERE : WHY YOU CAN T TRISECT AN ANGLE, DOUBLE THE CUBE, OR SQUARE THE CIRCLE. Contents. 1.

Homework 1 from Lecture 1 to Lecture 10

Summer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages

SIMILAR TRIANGLES PROJECT

June If you want, you may scan your assignment and convert it to a.pdf file and it to me.

MA 1125 Lecture 15 - The Standard Normal Distribution. Friday, October 6, Objectives: Introduce the standard normal distribution and table.

To Find the Product of Monomials. ax m bx n abx m n. Let s look at an example in which we multiply two monomials. (3x 2 y)(2x 3 y 5 )

Relationships Between Quantities

TRAINING LAB BLOOD AS EVIDENCE ANALYZING BLOOD SPATTER NAME

Student Instruction Sheet: Unit 3, Lesson 3. Solving Quadratic Relations

Copyright, Nick E. Nolfi MPM1D9 Unit 6 Statistics (Data Analysis) STA-1

System of Linear Equation: with more than Two Equations and more than Two Unknowns

Section 2. Locating Astronomical Objects in the Night Sky What Do You See? What Do You See? Think About It. Investigate.

MITOCW watch?v=ztnnigvy5iq

Grade 6 Math Circles. Ancient Mathematics

Around the corner. Mathematics B-day 2015, Friday November 13, 9:00h-16:00h

2.7 Implicit Differentiation and Related Rates Math 125

Roberto s Notes on Linear Algebra Chapter 11: Vector spaces Section 1. Vector space axioms

Unit 3 Right Triangle Trigonometry - Classwork

14.1 INTRODUCTION. Nature. Architecture. Engineering. Compose a picture-album showing symmetry. Make some symmetrical paper-cut designs.

VERTICAL PROJECTILE MOTION (LIVE) 08 APRIL 2015 Section A: Summary Notes and Examples

Angles Lab. name: Part I - How tall is Founders Hall? Astronomical Ideas, Fall 2012

2.4 Investigating Symmetry

This is a one-week excerpt from the Starfall Kindergarten Mathematics Teacher s Guide. If you have questions or comments, please contact us.

Note: Please use the actual date you accessed this material in your citation.

9.4 Radical Expressions

{ }. The dots mean they continue in that pattern.

Chapter Seven Notes: Newton s Third Law of Motion Action and Reaction

Transcription:

The Masonic Aprons - Geometrical Foundations Patrick G. Bailey, VIII Degree * Golden State College S.R.I.C.F. Los Altos, California August 23, 2015 Have you ever wondered where the designs of our Masonic Aprons came from? The true answers are probably lost in antiquity, sometime in the 1600s or 1700s, in Scotland or Europe. However, we can imagine the steps that our ancient brethren may or would probably have taken to design the Entered Apprentice, Fellowcraft, Master Mason, and Past Master aprons. Now today, we would all think that these aprons would look pretty much the same, as that is what we have learned in our experience, since the early 1900s. Most Masonic Lodges today probably have ordered their aprons from Masonic supply houses, which may have made up their own designs. Some Lodges may even be under the directorship of their Grand Lodge for the design of the aprons that they are to use. The Grand Lodge of California does not specify the geometrical design of the aprons that we use, so they seem to be all the same size and pure white, with the Past Master s apron having a blue fringe around the edges and the flap. But still, I ask, what was the original geometrical design? And why is it that, when you stand in front of the main doors to the Grand Lodge of England, you are found standing on a very large gold pentagram buried in the concrete sidewalk? Where did that come from? We are taught in the Masonic Degrees that we are to build our Masonic Superstructure in degrees, using horizontals, right angles, and perpendiculars. So, if we were to start our own Mystery School, and we were to assign a geometrical form to each degree, then we would probably choose for each increasing degree: (1) the square, (2) the triangle, and (3) the pentagon. We will now construct our Mystery School aprons for each degree from those shapes. The First Degree - Entered Apprentice The EA is told in that degree to stand with his feet forming the angle of a square. He is admonished to use the square as one his first working tools. It then makes sense that the EA apron would be in the form of a square. What then we do about the flap? We just add another square, rotated, as the flap, turned up, thusly: 1

Figure 1. The EA Apron Figure 2. The FC Apron The angle of the upward flap (to the horizontal) is then 45 degrees. The Second Degree Fellowcraft The FC is taught that Masonry is taught in degrees only, and that in his lecture there is a staircase of 3, 5, and 7 steps. The FC apron should be more complicated in form than the EA apron. Also, the FC apron must be easily distinguished from an EA apron whose flap may have fallen down. This is easily accomplished using an equilateral triangle whose flap is turned down, as shown above. To our eyes, this looks like the down-turned flap is too long, and that it maybe should have a downward angle of only 30 degrees, instead of 60 degrees. I argue against that, because an EA apron whose flap has fallen down would look very similar to such a 30 degree FC apron. A 60 degree apron allows a much better unique design where no such mistake can be made. The Third Degree Master The Master has shown to him all the Light that he can receive at this time. It then makes sense that his apron would follow the logical sequence and be based on a 5-sided figure, the pentagon. Drawing a pentagon on the top of the square gives us the Master s apron, thusly: 2

Figure 3. The MM Apron Figure 4. An Alternate MM Apron The angle of the downward flap is now 36 degrees, very close to the suggest 30 degree FC apron flap that we did not choose above. So we see that all of these aprons are easily distinguished, whether the Master wore his flap differently or not. To provide an additional level of distinction, a MM apron could also be folded with one corner attached to the apron top. The Past Master Degree and Apron Past Master In England, and in most of Europe, the PM Degree is given only to those Master Masons who have completed their service as Master of their Lodge, and they have successfully installed a successor. Many PMs know what educational process this can be! Sure It s easy, don t worry they said. Right. So you actually learned many things during your time as Master of your Lodge. You learned that things may look simple on the surface, yet to solve a problem, a greater depth of knowledge is needed in order to obtain a perfect solution. That is the task of the Past Master to learn to move toward being perfect. This far we have been using a square to construct our Masonic Superstructure. What would be more perfect for this PM Degree? How about use of the simple figure that most mathematicians and physicists agree is the perfect rectangle : the Golden Section, otherwise known as The Divine Proportion, which is the foundation of Sacred Geometry! [1] The Golden Section is that length x whose proportion is defined by: (x-1) = 1/x. This Golden Ratio of x:1 shows up most simply in the pentagram, the perfect five-pointed star the SECRET EMBLEM of many ancient metaphysical societies. Its value is simply: x = [1 + SQRT(5)]/2 = 1.618034 = phi 3

which is given the mathematical name phi. So we see that: phi 1 = 1 / phi; phi + 1 = phi^2, and so on. In a previous study, we have already seen that the use of this sacred parameter phi can be used to easily construct all of the symbols in the Masonic Degrees, and as well as all of the symbols in the York Rite. [2] By creating an apron with this shape (phi by 1), and adding the flap at a downward angle of 36 degrees, we see that we have defined upon our apron an exact pentagram! The horizontal arm of the pentagram is exactly the same as the top edge of the apron, and the flap corresponds exactly to the intersecting arms of the star. What could be the significance of that? Figure 5. The PM Apron Human Dimensions The internet gives us the dimensions of an average man that are used in most of the clothing industry, normalized to fractions so that the total height is 1. [3] I will not list all of the dimensions here. Instead, I will multiply all these dimensions by 72, to get the front view figure of a man 6 feet tall, thus having a waist of 13.752 inches across at a height of 38.160 inches above the floor. Wearing the Master Mason s Apron A good picture in relative dimensions of a man wearing the Master Mason apron above is shown below, where the width of the apron is set equal to this waist size. This appears differently than what most of us are used to seeing today. 4

Figure 6. Wearing the MM Apron Figure 7. Wearing the PM Apron Wearing the Past Master Mason s Apron A good picture in relative dimensions of a man wearing the Past Master s Mason apron in a similar manner is shown in comparison above. This looks more like what most of us are used to seeing today. It is more pleasing. This is probably why the Masonic aprons we see today almost always have a width to height ratio of 1.6 or 8:5 (close to phi), or 1.5 or 3:2. What significance can we apply to that pentagram star? We can see that by expanding the radiance from the star into the next level perfect star, as seen in Figure 8 below. Here I have added the next level star about the apron s inner star. We see that the outer star encompasses all of the vital points of man. The upper star point also exactly intersects the guttural perfect point of entrance. I have also included a square that exactly intersects the side points of this outer star. In addition, I have drawn four levels based on the geometry of that star, that divide man into the five zones. 5

Figure 8. Wearing the Radiance of the PM Apron 6

I can label those zones from the bottom up: Earth, Water, Air, Fire, and Ether (The Five Elements). [4] Note how these zones accurately describe the function of the body in those zones. I can also include two zone lines to define locations to create the seven chakras! [5] Now, note how the downward arms from the top of the outer star intersect with the square that intersects the outer star points. There lies the Square and Compass! Is it any wonder that when I visited the Grand Lodge of Scotland, that all of the compasses on display were all set at the angle of 36 degrees? The bottom of that square might be considered The Root of Freemasonry! Note also that the downward length of the apron also doesn t really matter! What matters is the position of the star, with its horizontal arm lined up across your waist! Wearing these aprons reminds you that you are seriously seeking perfection and that you are yearning for higher knowledge. When you put on your apron you are radiating Light! YOU ARE A STAR! In your personal quest to become more perfect and a better man, you may well remember: In this sign you shall conquer. References 1. The Divine Proportion A Study in Mathematical Beauty, H. E. Huntley, Dover Publications (paperback book, 186 pp.), 1970. 2. A View of Masonic Sacred Geometry, Golden State College SRICF Presentation, August 22, 2004, http://www.padrak.com/paperfiles/bailey_082204_rev_1.pdf. Also published in Published in the SRICF Annual Review Ad Lucem 2007, pages 53-74. 3. Human Dimensions (Normalized to height 1), https://search.yahoo.com/yhs/search?p=human+man+dimensions&ei=utf- 8&hspart=mozilla&hsimp=yhs-001. 4. Five Elements, https://en.wikipedia.org/wiki/five_elements. 5. Introduction to the Chakras, http://www.eclecticenergies.com/chakras/introduction.php. 7

* Patrick Bailey is the Secretary of Golden State College in northern California. He became a Mason in Los Altos Lodge in 1993, and has been very active in Masonry and York Rite Masonry. He was Master of that Lodge in 1999. In the York Rite bodies, he received the Knight York Cross of Honor in 2006, and the Knight Templar Cross of Honor in 2013. He can be reached at pgbmason@sbcglobal.net. 8