S. Berliner, III's Labyrinth Continuation Page 1 keywords = labyrinth labyr labrys path circuit rosette petal lunation cusp foil turn quadrant classical medieval Chartres maze garden

Updated:   30 Oct 2016,  12:15  ET
[Page created 16 Nov 2013;
    original AT&T Worldnet Website begun 30 May 1996.]

URL:  http://sbiii.com/labyr-01.html

S. Berliner, III
Consultant in Ultrasonic Processing
"changing materials with high-intensity sound"

[consultation is on a fee basis]

Technical and Historical Writer, Oral Historian
Popularizer of Science and Technology
Rail, Auto, Air, Ordnance, and Model Enthusiast
Light-weight Linguist, Lay Minister, and Putative Philosopher



note - The vast bulk of my massive Web presence (over 485 pages) had been hosted by AT&T's WorldNet service since 30 May 1996; they dropped WorldNet effective 31 Mar 2010 and I have been scrambling to transfer everything.  Everything's saved but all the links have to be changed, mostly by hand.  See my sbiii.com Transfer Page for any updates on this tedious process.


S. Berliner, III's

Labyrinth

Continuation Page 1


PAGE INDEX:

[Please note that I rearranged the main page and this first continuation page and added
    a second continuation page on 09 Jun 2015 to balance out the coverage better.
 Accordingly, I have removed all prior NEW and REV'D icons.]

On the Main Labyrinth Page (16 Nov 2013):
    Introduction to the Labyrinth.
    Labyrinth Terminology.
    The Chartres Labyrinth.
    Designing a Labyrinth.
    Miniature and Finger Labyrinths.
    Building a Garden Labyrinth.
    Building a Deck Labyrinth. (moved to Continuation Page 2 on 09 Jun 2015).
    Building a Tape Labyrinth (moved to Continuation Page 1 on 16 Nov 2013).
    Glastonbury Tor Labyrinth?   new (30 Oct 2016)
    Labyrinth Links.
    Redwood Shores Labyrinth (moved to Continuation Page 1 on 09 Jun 2015).

On this Labyrinth Continuation Page 1 (moved from main page 16 Nov 2013):
    Building a Tape Labyrinth (moved here on 16 Nov 2013).
    Chartres Labyrinth Proportions and Dimensions.
    Nominal Dimensions and Precision.
    Redwood Shores Labyrinth (moved here on 09 Jun 2015).
    Grace Cathedral (S.F.) Labyrinth.   added (24 Oct 2016)
    Armenian Heritage Park Labyrinth.   new (09 Jun 2015)
    Clark Estate Labyrinth {???}.   new (27 Jul 2015)

On Labyrinth Continuation Page 2:
    Building a Deck Labyrinth. (moved from main page on 09 Jun 2015).


[Please note that illustrations shown on this page are all, unless otherwise noted, from Wikipedia or other public domain sources.
My gratitude to Jeff Saward of Labyrinthos for permission to reproduce drawings and a photograph from his site.
My gratitude also to Robert Ferré and LG Moriarty for helpful advice.]

Let us now turn from how many angels can dance on the head of a pin to how to create a tape labyrinth.



Building a Tape Labyrinth (some tips) - I have made several fairly large masking tape labyrinths in churches; usually in a big hurry.  The big trick here is to fabricate a removable center pivot which can be taped down and used with a marked cord to walk the tape around without marking the floor.  After the circles are taped down, the pivot can be pulled up and repositioned to lay out each petal in the rosette (although eyeballing usually is more than good enough).

Another tape trick is to NOT leave the tape down too long (or face the wrath of the custodian)!

Some images:

TapeLabyPivot
Tape Labyrinth Pivot

04 Jun 2015 Sketch by and © 2015 S. Berliner, III

[The actual pivot seems to have vanished so I cooked up this sketch -
the base could be a piece of plywood, with a length of dowel or broomstick nailed or screwed to it.]

Here are three cell-phone snapshots of a "quickie" 20' (6m) masking tape labyrinth I helped parishioners build at First Parish in Cambridge (taken under appalling lighting conditions):

FPC04 FPCo4 FPC40
(12 May 2013 photographs by and © 2013 S. Berliner, III)
First Parish Cambridge Tape Labyrinth



PROPORTIONS AND DIMENSIONS OF
THE CHARTRES LABYRINTH

Robert Ferré gives exact proportions and dimensions of the actual Chartres labyrinth on the Proportions page of his Labyrinth Enterprises site; I have taken the liberty of reproducing them here (ever-so-slightly edited and formatted but this is Robert Ferré's work, NOT mine!):


PROPORTIONS OF THE CHARTRES LABYRINTH

The labyrinth reflects deliberate principles of sacred geometry, especially regarding the numbers three (trinity, soul, divine) and four (body, earth, this world).  These two numbers can be combined, symbolizing the integration of body and spirit, physical and divine.  Added, they give seven and multiplied, they give twelve.  Both numbers are important to the Chartres labyrinth.

To draw the 11 circuits (paths) in the labyrinth requires 12 circles.  Below is a summary of the proportions of the labyrinth as determined by Robert Ferré.  Agreement on this subject is far from universal.  For example, Robert has determined that Keith Critchlow's oft-repeated theory of an invisible 13-pointed star in the labyrinth is incorrect.  Because the stones are worn and there is mortar between them, measuring the Chartres labyrinth is rather complicated.  The proportions below are a composite taken from careful examination.  If you follow these specifications exactly, there will still be an error somewhat under one percent with regards to the actual labyrinth.  But that's pretty close.

The measurements below take into consideration that lines have width.  In Chartres Cathedral, the lines of the labyrinth are three inches wide.  Therefore, there is an inside and an outside dimension of each line, which is to say, one side is closer to the center and the other side, further away (and therefore, slightly larger).  The proportions will specify to what part of the line the measurements pertain . "Inner" or "inside" mean closer to the center;"outer" or "outside" mean the opposite (further away).

Center Circle: The center is one-fourth the diameter of the labyrinth, measuring from the outside of the center circle to the outside of the 12th circle (not including the lunations, the small partial-circles around the perimeter).

    Example: The labyrinth is 36 feet in diameter, the center is 9 feet.

Petal: The outer petal circle is one-third the diameter of the outer center circle.  (Note the fours and threes.  The center is one-fourth, the petals are one-third.  Could the center be this world, and the petals represent Mary?)

    Example: The center is 9 feet in diameter, the petals are 3 feet.

Path: The width of the path, not including the line, equals one-third the diameter of the petal.

    Example: The petals are 3 feet in diameter, the path is 1 foot wide.

Line: The width of the line is very important.  The line and path together comprise 11 units, of which the line equals two units and the path nine.  Once you have the path width, you can divide it by 4.5 to get the line width, or divide it by nine (which gives one unit) and multiply that result by two (hence, two units).  In other words, divide the path width by nine and multiply that number by two and you will find the line width.

    Example: Path equals 12 inches. Line equals 12 divided by 4.5, or 2.67 inches (slightly under 2 and 11/16 inches).

    Alternate calculation: Path equals 12 inches. Divide by nine to get one unit (1.33 inches) and then multiply by two, which gives 2.67 inches.

Lunation: The spacing of the lunations (the circles around the perimeter, measured mid-circle to mid-circle) equals the width of the path (example: 12 inches),  However, the lunations require a little fudging, in order to get a tooth at the very top, on the vertical axis.  As a result the lunations on the left side are slightly closer together and the ones on the right side slightly further apart.  The top tooth is number 56. There are 55 lunations on the left side and 57 on the right side, for a total of 113 teeth.  The teeth on either side of the entrance are half the path width from the entrance (example: 6 inches).  Want to be more mathematical?  Calculate the circumference and divide by 114.  This will find the spacing on the 12th circle, rather than through the center of the lunation circles.  The diameter of 36 feet equals 432 inches.  Times pi (3.14159), we get a circumference of 1357.17 inches.  Dividing by 114, we get 11.9 inches, or about 3/32 short of our previous estimate of 12 inches.  As I said, this number should be a bit smaller on the left side and a bit larger on the right (by 1/8 to 3/16 inches).

Note that the path width is one-third of the petals which are one-third of the center which is one-fourth of the diameter of the labyrinth.  That comes out to being 1/36 the diameter of the labyrinth.  If you have a Chartres labyrinth that does not follow the correct proportions, you won't be able to calculate the lunations by the method given here.  Instead, just divide the diameter of the labyrinth by 36 and use that measurement for your spacing (not counting the minor fudging).

Although Robert has given an example, these measurements apply to any size Chartres labyrinth.  If the diameter is 60 feet, the center is 15 feet, etc.

EXACT MEASUREMENTS OF THE CHARTRES LABYRINTH

Periodically Robert receives a call from someone who wants to make an exact-size replica of the Chartres labyrinth.  Here are the actual measurements as he has personally made them in Chartres Cathedral:

Diameter from tip of tooth to tip of tooth: 42' 3 3/8"

Diameter to outside of 12th circle, not counting lunations: 40' 4 5/8"

Diameter of center (to outside edge of the first circle): 10' 1 1/4" (121 1/4")

Petal diameter: 40 1/8"

Path width: 13 5/8" to 13 3/4"

Line width: Varies from 3" to 3 1/4" but most are close to 3"

Space between labryses (back-to-back turns): 3" to 3 1/2".  Robert would use 3 1/4".

Lunation: Inside diameter of the circle: 11"

Lunation, total width: 13 3/4" (measured through the center of the circle, from mid-tooth to mid-tooth).

[Please allow me to remind you once again that these proportions and dimensions are the work of Robert Ferré, NOT mine!)]



NOMINAL DIMENSIONS and PRECISION - where Robert Ferré is an artist, I am a technologist (an almost-but-not-quite Mechanical Engineer).  As such, I am more concerned with exactitude.  In science, engineering, and technology, we find the average and the mean of varying dimensions and come up with "NOMINAL" dimensions, those single numbers that best describe the range of numbers with which we are faced.  Thus, where Robert might write, '13 5/8" to 13 3/4"', I am more likely to write '13-11/16" nominal' or '13.6875" nominal'.  No uneven lunations for me!  Mine are calculated and laid out with insane precision (and then drawn/painted with abandon, anyway)!  :ˇ)

I should point out here a similarity between this sort of over-doing things and so-called "armchair railroading" (in the modeling sense), both of which are, in some ways, an avoidance regimen; it's easier to work on drawings than on the real thing.  Get the overall dimensions right and then jump right in and eyeball the details!

More specific coverage of how I applied all this "precision" (fanaticism?) to my home deck labyrinth has been moved to Building a Deck Labyrinth / Recalculated Lunations on Continuation Page 2 on 09 Jun 2015).


Where on the east and west coasts (of the U. S.) can one can find typical large outdoor labyrinths open to the public?  Here are some prime examples:

- - - * - - -

Redwood Shores Labyrinth

My younger daughter worked in the EA Business Park in the Redwood Shores area of Redwood City, California.  In a beautiful park-like setting between large office buildings, an enlightened developer set a large (~75'?) packed-bare-earth Medieval labyrinth, nestled in lush grass.  It's in the triangle formed by Redwood Shores Parkway, Shoreline Drive, and Twin Dolphin Drive, immediately southwest of the midpoint of the EA Bikeway and just north-northeast of a big circular path.  Visiting there on 10 Nov 2013, I was so impresseed that I took a series of shots:   movehere (09 Jun 2015)

North across circle towards labyrinth area (L); first view of labyrinth (C); and cresting small hill (R):
Redwoodo3 Redwood03 Redwood04
Redwood Shores Labyrinth (click on thumbnailed pictures for larger images)
(10 Nov 2013 photographs by and © 2013 S. Berliner, III)

Almost there. (L); the entrance and plaque (C); and detail of the plaque (R):
Redwoodo4 Redwood06 Redwood07
Redwood Shores Labyrinth (click on thumbnailed pictures for larger images)
(10 Nov 2013 photographs by and © 2013 S. Berliner, III)

The center - an 18" bronze snail (L); the snail - head on.(C); and looking back (R):
Redwood08 Redwoodo8 Redwood11
Redwood Shores Labyrinth (click on thumbnailed pictures for larger images)
(10 Nov 2013 photographs by and © 2013 S. Berliner, III)

Walking back toward the office, here's a bucolic view looking northwest:

Redwood13
Redwood Shores Labyrinth (click on thumbnailed picture for larger image)
(10 Nov 2013 photograph by and © 2013 S. Berliner, III)

To help you locate the Redwood Shores labyrinth, I append marked satellite photography:

RedwoodShores5m
[5000-foot resolution]

RedwoodShores2m
[2000-foot resolution]

RedwoodShores1m
[1000-foot resolution]

RedwoodShores5c
[500-foot resolution]

RedwoodShores1c
[100-foot resolution]

RedwoodShores20
[20-foot resolution]

RedwoodShores10
[10-foot resolution]

- - - * - - -

Grace Cathedral (S.F.) Labyrinth

On the main Labyrinth page, under The Chartres Labyrinth, I note that, thanks to the Rev. Dr. Lauren Artress, Grace Cathedral (Episcopalian) in San Francisco has TWO Chartres labyrinth reproductions one of terrazzo in the pavement out front and a limestone one inside.  Let's take a quick look down on the outdoor one:   added (24 Oct 2016)

GraceSF100
[100-foot resolution]

GraceSF20
[20-foot resolution]

- - - * - - -

Armenian Heritage Park Labyrinth

Jumping from the West Coast to the East Coast, there is a beautiful labyrinth on the Rose Kennedy Greenway in downtown Boston, close by Faneuil Hall and the waterfront, in Armenian Heritage Park,  My wife and I have walked it several times before but, on 02 May 2015, we attended the combined World Labyrinth Day: Walk as One at 1 (Coming Together on Common Ground in Peace and Harmony) and a ceremony and walk honoring Armenian heritage and had a wonderful time.   new (09 Jun 2015)

ArmenianHeritagePk1
Armenian Heritage Park Labyrinth from Above

It's a unique design, a circular winding path paved in grass and inlaid stone, celebrating life's journey:

ArmenianHeritagePkDesign
Armenian Heritage Park Labyrinth Design

a modified 60' (18.3m) Medieval in granite, designed by Donald J. Tellalian (note the typical Armenian name), AIA, and built by Barletta Heavy Division in May 2012.  A single jet of water in its center represents hope and rebirth.  ART, SERVICE, SCIENCE, and COMMERCE are etched around its circle in tribute to Armenian-American contributions made to American life and culture.

ArmenianHeritagePk2
Armenian Heritage Park Labyrinth at Dusk

Directly adjacent to the labyrinth is a monument commemorating the Armenian genocide of 1915-1923 (and others); atop a gentle overflow fountain sits an abstract sculpture, a split dodecahedron; annually in late March it is reconfigured by having a crane lift and pull apart the two halves of the split dodecahedron, made of steel and aluminum, and reshape the two halves of the geometric shape into a new and different sculpture:

ArmenianHeritagePk3 ArmenianHeritagePk5 ArmenianHeritagePk4
Armenian Heritage Park Labyrinth Sculpture

The inscription reads:

Boston and the Commonwealth of Massachusetts have offered hope and refuge for immigrants seeking to begin new lives.
The park is a gift to the people of the Commonwealth and the City of Boston from the Armenian-American community of Massachusetts.
This sculpture is offered in honor of the one and one half million victims of the
Armenian Genocide of 1915-1923.
May it stand in remembrance of all genocides that have followed, and
celebrate the diversity of the communities that have re-formed in the safety of these shores.

The overflow fountain is a reflecting pool; its waters pour over the sides and re-emerge as a single jet of water at the labyrinth's center.

ArmenianHeritagePkFountain
Armenian Heritage Park Labyrinth Fountain

Photos by Matt Conti and Peter Vanderwarker from the Armenian Heritage Park site - all rights reserved.

As I added above for the Redwood Shores labyrinth, I append similar satellite photography to locate the Armenian Heritage Park labyrinth:

ArmenianHeritagePk5c
[500-foot resolution]

ArmenianHeritagePk2c
[200-foot resolution]

ArmenianHeritagePk50
[50-foot resolution]

ArmenianHeritagePk20
[20-foot resolution]

ArmenianHeritagePk10
[10-foot resolution]
Armenian Heritage Park Labyrinth Location

C'mon down - try it; you'll liiiike it!  Bring the kiddies - there's a classic carousel right next to the labyrinth (you can see it on the 50' satellite photograph above, just across Mercantile Street).


On 27 Jul 2915, I ran across a news item about Bellosguardo, the late Huguette Clark's grand Santa Barbara estate, miraculously-untouched since the 1950s, and this aerial photo:   new (27 Jul 2015)

Bellosgardo
[Arrow by S. Berliner, III]

At first glance, that sure looked like a magnificent labyrinth (red arrow) in a gorgeous setting!  Well, let's look again:

Be;losgardo2 BellosgardoX
[Left - Actual "fancy"*  ||  Right - labyrinth by and © S. Berliner, III - 27 Jul 2015]
(* - in the old English landscaping/architectural sense)

I found a slightly different aerial view:   added (24 Oct 2016)

Bellosgardo1

Naturally (for me), I had to fiddle with that view as well:

Bellosgardo1X
[Labyrinth by and © S. Berliner, III - 24 Oct 2016]

The hedge at the back had to be shifted a wee bit and we have to wait for the rest of the bordering hedges to grow some so we can clip the lower branches to make room for the outer course, of course.

And again!  Yet another:

Bellosgardo3

Fiddle we must:

Bellosgardo3X
[Labyrinth by and © S. Berliner, III - 24 Oct 2016]

O. K.; so we can't have everything our way - but it sure WOULD be nice my way!



Continued from main Labyrinth page and on Labyrinth Continuation Page 2.



LEGACY

  What happens to all this when I DIE or (heaven forfend!) lose interest?  See LEGACY.

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See Copyright Notice on primary home page.



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