WATER THAT SINK TRAP

This is something you might not have read anywhere else.

If you have a sink in your house that is not used very often, you need to pour water down the drain from time to time to fill the trap under the sink.  (The trap is that curved piece of pipe under the sink.  Because it is curved, it traps a bit of water in the pipe.)

It is important to keep the trap filled with water.  Why?  The water acts as a plug to keep sewer gases from coming up from the sewer pipes into your house.  The water in the trap will evaporate over time, thus you need to replenish it regularly.  You’ll know if you’re overdue for a refill if you notice an odor.  Oh, by the way, this also applies to other fixtures in your house such as toilets, showers, or tubs that typically have traps under them.  (Some traps may be under the flooring where you can’t see them.)

My house is average-sized, but nevertheless, there are a couple of sinks that get very little use.

Strange that I have to perform this ritual of watering the traps.  But nice, too.  In a way it’s comforting to do these little tasks.  Not much of a bother really.  I do it right before I make up a new pitcher of my special lemon-orange drink (two squeezed lemons, three cups of orange juice, three or four cups of water).  That way, it always gets done.

Bringing order out of chaos (draw it)

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Little chores are much better than having to deal with disasters and emergencies, and the inevitable next problem coming down the line.  The 34,000 dead in the China earthquake can no longer water their traps (Sichuan province, May 12, 2008).  The 100,000 dead in the Burma cyclone are beyond such cares (Cyclone Nargis, May 3, 2008).  Many of the almost 250,000 Chinese injured in the earthquake and their neighbors are stressed beyond belief.  And I wrote that before today’s headline:  “A powerful aftershock destroyed tens of thousands of homes in central China, causing hundreds of new casualties Sunday and straining recovery efforts from the country's worst earthquake in three decades.”

Yes, I had a stress filled two weeks, but I’ll guess not as bad as someone else’s.  So I’ll get back to my routine tasks, like watering the sink traps.  It’s soothing. 

Writing my little post is soothing.

Slide show and music on my main page.

-2008-

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THE SEASONS TURN

One season follows another.

The season for weeding and clipping is now in full swing in my yard.  Everything needs to be done at once.  Done now.

In these perfect days of springtime I try to notice everything.  To be in tune with the seasons.  To drink it all in.

Why try to be observant and notice everything?  Why not?  I sure don’t want to miss anything.

I try to notice each and every flower.  If I don’t know the name for a flower, I make one up.  In recent days I have noticed these flowers:

Bluets, yellow flowers of false strawberry, pink phlox, periwinkle, yellow sheep sorrel, lily-of-the valley, dandelions, strawberry flowers, wild asters, buttercups, dogwoods, six-pointed yellows, barberry, violets, bugle, southern blue flag, rose-of-Sharon, Siberian iris, pea plant flowers, peony, masses of white, pink, and red azaleas, more than a hundred daisies. 

What have you noticed lately?

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I found the first bit of poison ivy.  I’ve found deer ticks on my clothes.  (Ticks carry disease.)  Sometimes it is critical to be observant.

I remember, vaguely, reading about an exercise in being observant.  A teacher gave her students the task of visiting a nearby museum, selecting one display item in the museum, and then spending what, an hour? each week for many weeks, just observing that one item, and recording observations.

Can one sharpen one’s observation skills?  I don’t know.  One can always observe more.

In these perfect days, I notice how the temperature is perfect.  No need to heat or cool the house.

I notice how some plants prefer to grow in my driveway rather than in my garden.  Perhaps because of the moisture accumulated under the gravel.

The daisies grow profusely alongside the large stones bordering the front circle garden and near the brick border by the sidewalk, where their roots can be sheltered and moist.  They grow so well because I weed around them.

I notice how the plants respond to the rain.  How fresh and lush everything looks after a rain.

I notice the pitter-patter sound of rain as it begins.  I notice the fluorescent electric green glow of the forest in the cloud-dimmed light.

I notice the lovely shade of green of the moss in springtime.

The season for planting seed has come and gone.  One of the most difficult tasks.  I remember noticing how the sun lit up the green grass while I planted.  Made it look like it was lit from within.

I noticed the wind tossing the leaf covered boughs of the tree in the front center of my yard.  When did the tree buds become leaves?  It all happened so quickly.  I forgot to notice.

How quickly everything grew up this year.  Are the seasons turning faster by any chance? 

I didn’t notice the clematis until it was knee high.  Now it is more than six feet high on its trellis.  Seemingly grew overnight.

I notice every glorious, rare and precious moment of complete silence, when there is no distant rumbling of trucks on the highway, no screeching of neighbors’ heat pumps, no dog’s incessant barking, no weird music being broadcast from the next subdivision, no morons setting off firecrackers, no adolescent males roaring up and down the road on their motorized scooters, etc.  A silence punctuated only by the welcome calls of birds, the sound of a gentle breeze in the leaves of the trees, and the joyous shouts of children.

I used to try to distinguish the bird calls.  But didn’t have much success with that.  I could differentiate a few dozen I suppose (mostly I had to make up names for the different birds), but gave that up.  The call of the pileated woodpecker is distinctive though and easy to remember.  I like to notice that.  And the drum-roll of pecking.

I notice the buzzing and twittering of the insect and amphibian chorus – seems to be getting less raucous.  Why?

I notice the march of weeds across my lot.  New species yet again this year.  Why?  Climate change?  Or just the progression of succession – this lot was cleared only ten years ago. 

I’ve noticed how the snow line is moving past us to the north.  Easy to notice climate change from this vantage point.  I notice that the pea plants can more easily self-seed.  The parsley didn’t mind the winter this year at all.  In the past couple of years, the season for weeding has lingered on through the season of winter.  No rest for the weary now.

I noticed where a deer has nibbled hosta leaves.  Strange – usually they only go for the hosta flowers.  Are the deer getting hungrier?  

I drink in every butterfly.  My impression is their numbers are dwindling, and I am just stunned by how few there are now.  The garden seems so sterile without lively butterflies flitting about.

Life is a merry-go-round, but the reoccurring event of springtime is one I don’t mind re-living again and again.  I’ll notice every little thing.

Slide show and music on my main page.

-2008-

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DRAWING THE “JESUS TOMB” SYMBOL, PART 11

I was wondering how to rotate the tomb symbol angle so its ends would join up and make a star.

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, and Part 10.

Actually, once I figured out how to rotate the tomb symbol angle to make a 6-pointed starburst, I realized how simple it is.  When the angle opens outward, and the ends are anchored in two corners of an equilateral triangle, with the third corner anchored at the center of the standard circle which gives rise to the hexagram which gives rise to the equilateral triangle, and the angle is rotated in increments of 60 degrees, then you get a starburst, as shown in the following image.  The peripheral sides of the equilateral triangles now comprise the six sides of a hexagon.  The 6 tomb symbol circles are included with position relative to the 6 tomb symbol angles unchanged.

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I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

In the following image, I included a hexagram (navy) in the design and also increased the rotations to increments of 30 degrees, yielding a 12-point starburst constructed from the lines of the tomb symbol angle (pale green lines, lavender-filled).  The 12 tomb symbol circles are included with position relative to the 12 tomb symbol angles unchanged.  The tomb symbol’s position relative to its contextual hexagram is unchanged.

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The following image got rather busy as I added pentagrams (red), anchored on the center of my standard circle, and rotated in increments of 30 degrees, and added tomb symbols rotated in increments of 6 degrees.  Pentagram lines and hexagram lines (navy) scoot outwards from the center and pass between tomb symbol circles very close, but not tangential to them.  Some of the joined ends of tomb symbol angles (pale green) meet on pentagram lines.  Some tomb symbol circles intersect on pentagram lines.   Some tomb symbol circles intersect with hexagram lines at pentagram lines.

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In the following image, the 12-point starburst described earlier becomes a 24-point starburst (dark green) as the tomb symbol angle is rotated in increments of 15 degrees.  Tomb symbol angles opening outward are placed at several levels, each successive level adding one-fourth the diameter of the standard circle.  Level 1 (pale green) is anchored on the center.  Tomb symbol angle lines level 3 (purple) intersect at the apex of tomb symbol angle level 4 (pink).  Tomb symbol angle lines level 1 (pale green) end at or about tomb symbol angle lines level 3 (purple).

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In the following image, the tiers of tomb symbols are rotated in increments of 5 degrees, each successive level adding one-fourth the diameter of the standard circle.  Tomb symbol angle lines intersect at intersections among tomb symbol circles in tier 2.  Tomb symbol angle lines end at tomb symbol circles in tier 3.  Tomb symbol angle lines intersect at the interface between tier 3 and 4 circles.  In tier 4, the ends of tomb symbol angles join together.  Tomb symbol angle lines intersect at the centers (red, where visible) of tomb symbol circles in tier 5.    Tomb symbol angle lines intersect at or near the outermost points of tomb symbol circles in tier 6.  (See red arrows - click on "Full-size" below.)

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The tomb symbol, its circle and its angle, continue to be a font of inspiration and ever-evolving forms.  I am amazed.  Continued here.

-2008-

Slide show, music, and folders on my main page.

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

 This post was updated on July 28, 2008.

DRAWING THE “JESUS TOMB” SYMBOL, PART 10

I got the urge to draw some more circles.  This time starting with a six-petal flower, six circles rotated about a central circle, all circles the same diameter.

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, and Part 9.

In the following image, my six-petal flower became 12 petals when I copied/rotated/pasted the design 90 degrees.  The 12 circles are “green circles,” that is, the same diameter as the central circle (turquoise/regular blue, my standard circle), with centers on the standard circle, and intersecting the center of the standard circle.  I was a bit surprised to notice that each of the 12 circle centers lies on the intersection of a neighboring circle and the standard circle, until I remembered that in a six-sided hexagon the interval between corners is the radius of the enclosing circle.  The 12-pointed pale green-filled rosette is made from the “green circles.”  Notice how the borders of the tips of the rosette petals meet at the standard circle. 

The 12 indigo-filled circles are tomb symbol circles (one-fourth the diameter of my standard circle).  These 12 circles are likely not tangential to the “green circles,” but are nearly so, and each tomb symbol circle nestles closely within four “green circles.”  Each “green circle” passes close to four tomb symbol circles.  Each of 12 pink-filled half tomb symbol circles (one-eighth the diameter of my standard circle), is tangential to three “green circles.”  Each “green circle” is tangential to three half tomb symbol circles.

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In the following image, I stripped away the green circles, and added 12 “yellow circles” (gold-rimmed and partly yellow-filled, and three-fourths the diameter of my standard circle).   Each “yellow circle” is tangential to two tomb symbol circles (regular blue-filled) and two half tomb symbol circles (deep pink-filled).  After that, I added a central royal circle (royal blue rim, navy-filled, concentric with my standard circle (regular blue), and one-third the diameter of my standard circle).  This royal circle is tangential to the 12 “yellow circles.”  I added a wreath of 12 royal circles (royal blue rims, partly navy-filled, and one-third the diameter of my standard circle), each tangential to the standard circle and tangential to a tomb symbol circle.

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In the following image, the basic design is rotated at intervals of 6 degrees.  The outer coil is composed of 60 tomb symbol circles (black-green).  The inner rosette is also composed of 60 tomb symbol circles.  The pale green lines are tomb symbol angles; one anchored at the topmost point of the standard circle (regular blue) and opening downward (similar to the exercise in Part 2); the second anchored at the same point and opening upward. 

A pink circle, likely only visible in the full-size image, is inscribed through the innermost points of the outer coil of 60 tomb symbol circles.  Notice how the pale green tomb symbol angle lines intersect each other at that pink circle.  Wow!  When the circle is larger than the screen and the software won’t deliver a diameter sized one pixel smaller, then I have to improvise, which I did – this pink circle is derived from a section that fits at 9 and 12 o’clock, copied, rotated, and pasted into four quarters.

I couldn’t help but notice that a half royal circle (royal blue and one-sixth the diameter of my standard circle) will fit in the lattice made by the tomb symbol angles, fit so that the circle is tangential to four tomb symbol angle lines.  I couldn’t resist adding 20 such half royal circles.

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I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

In the following image, I used my 12 “green circles” flower.  I superimposed hexagons, both upward pointing and side-pointing (red), on each “green circle.”  I am awed that there is not a single point where “green circles” intersect that is not also an intersection point where red hexagon lines intersect.  Wow!  What a masterful design from the Great Designer!  Notice that some hexagon sides form perfect squares within the drawing.  I’ve added 48 tomb symbol circles (black-green) to the squares, each circle tangential to four sides of a square.  I guess I can catch a glimmer of why the circles fit the squares, but I still think it is marvelous.

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Since I started this series with a hexagon, I feel right at home here.  Continued here.

Slide show and music on my main page.

-2008-

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

DRAWING THE “JESUS TOMB” SYMBOL, PART 9

Jacob had a dream of angels going up and down a ladder.  A ladder that reached to the door of heaven (Genesis, chapter 28 NIV).

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, and Part 8.

What do I know about Jacob’s ladder?  That angels go up and down the ladder.  Well, assuming that “angels” are pentagrams, (and this has worked for me before, when I assumed Ezekiel’s “cherubim” were pentagrams (Part 2)), then the pentagrams should be pointed both up and down.  I am assuming the “ladder” is a repeating design that can be repeated endlessly, as far as “heaven.”

In the next image, I am starting my ladder with a hexagram (navy), an upward pointing pentagram (pink), and a downward pointing pentagram (green).  Notice the two horizontal lines of the hexagram and that each pentagram has a horizontal line – these will form the basis for my ladder.  Notice that the pink pentagram intersects the green pentagram at the horizontal line of the hexagram.  Wow!

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In the next image, I make my ladder by copying the image above and pasting it back on so that the top hexagram horizontal covers the nearest pentagram horizontal.  I do this a few times, repeatedly pasting the hexagram horizontal over the next pentagram horizontal, and notice that the circle centers are falling on points where pentagram lines crisscross the vertical diameter of the enclosing circle.  And as I continue, I notice that the lines of the green pentagram that crisscross the vertical diameter, cover (that is, coincide with) the lines of the pink pentagram that crisscross the vertical diameter – cover almost completely near this diameter!  Only a few pink pixels stick out.  My upward and downward “angels” overlap!!!  As I continue, the circle centers become covered by crisscrossing pentagram lines.  Circles intersect where some hexagram lines intersect.

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Broader view

I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

Here is a close-up of the pink pixels sticking out (8X magnification).

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Here I have re-colored my Jacob’s Ladder to emphasize the steps of the ladder:

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Have I discovered the real “Jacob’s ladder”?  I don’t know.  How could I possibly know?  I was so fascinated by it all, I was tempted to wrestle with it all night long, just like Jacob wrestled with an angel or divine messenger all night (Genesis, chapter 32 NIV). 

It seems to me there could be many different ways to draw a Jacob’s Ladder.  Think of the horizontal and vertical lines in a rotated hexagram (rotated 90 degrees to make a 12-point star).  Think of the horizontal and vertical lines made by pentagrams rotated 90 / 180 / 270 degrees.  These lines make rectangles and squares as shown in the following image.  These rectangles and squares can be assembled numerous ways to build fabulous designs.

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In fact I had been playing with my rectangles when I got the idea to build some stairs with them.  Then the idea of stairs reminded me of a ladder I had seen on a DVD in recent days.  A stone ladder sculpted on the exterior of a church in Bath, England, with winged angels going up and down – Jacob’s Ladder.  But nothing really worked for me until I examined the following design I made, placing pentagrams over the “Jesus Tomb” symbol to see how and what they would intersect. 

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Then I noticed that the upright and upside-down pentagrams meet at the hexagram’s horizontal.  Here’s a short list of interactions that can be found among the forms in this design:

1- Pentagram 1 (red-brown, downward pointing) meets the red line at the tomb symbol circle (black-green).

2- Pentagram 2 (purple, upward pointing) meets pentagram 1 at the hexagram’s horizontals,  meets pentagram 1 at the tomb symbol angle (pale green), and meets the yellow circle at the green circle.

3- Pentagram 3 (pink, right pointing) meets the red line at the hexagram, meets itself at the tomb symbol angle, meets pentagram 1 at about 3 o’clock on the tomb symbol circle, meets pentagram 1 at the green circle, and meets pentagram 2 at the green circle.

4- Pentagram 4 (gold, left pointing) meets pentagram 3 at the 12-point star’s verticals, meets itself at the tomb symbol angle, meets pentagram 1 at about 9 o’clock on the tomb symbol circle, meets pentagram 1 at the green circle, meets pentagram 2 at the green circle.

I’ll add a caveat here that I’m not convinced I have the perfect pentagram yet.  I’ve drawn pentagrams a number of different ways:  first with compass, protractor, and scanner; next by fitting lines around an inner concentric circle; and then by using software to rotate points around a circle.  If my pentagram is off by even one pixel, much of what I wrote above will be incorrect, will vaporize like morning dew in the sunlight.  (For instance, re-sizing the whole pentagram so its horizontal bar is one pixel closer to the circle center means no more ladder.)  Certainty awaits that perfect software.

I should tell you I started down this path, a detour really, a few months ago when I started re-drawing my forms with narrower lines.  Now I’ve learned that even a perceived setback can be a blessing if you find angels along the way.

I’m glad to have found my ladder with angels going up to heaven and down.  I’m so glad to have made this discovery on my own.  If this had been spoon-fed to me in a classroom setting, it might have been such a bore; but this way, on my own, I’m in drawing heaven, surrounded by angels.  Continued here.

Slide show and music on my main page.

-2008-

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

DRAWING THE “JESUS TOMB” SYMBOL, PART 7

I looked some more for a “square,” playing with what I am calling my “orange lines.”  These are lines that are 45 degrees off the vertical, which can form diamond-shaped squares. 

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, and Part 6.

I was inspired in part by a design of “sails” carved in rock by ancient Polynesian seafarers shown in the National Geographic.  I still do not have a clue what the sails could signify or how to make them, but after many attempts at arranging circles and orange lines to make sails, I came up with the grid shown in the following image: 

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My orange line starts at the upper left corner of the hexagram (navy), meets a lower right corner of the 12-point star (gray), takes a sharp right (right angle) at that point and meets its mirror coming from the other way at a point directly under the center of the enclosing circle (circle 1, regular blue).  That point becomes the bottommost point of circle 2 (regular blue), and the center of circle 2 is where the orange line and its mirror intersect within circle 1.  The diameter of circle 2 is the same as circle 1.  With circle 2 established, I continued to work on the grid, extending the orange lines up to the sides of circle 2, taking a sharp right angle turn at the sides, making a perfect diamond square within circle 2. 

Take a look at how the orange lines intersect at the “green circle,” at the point where lines of the hexagram and 12-point star intersect (red arrows).  Amazing!!!  (The “green circle” is the top circle in the image, the same diameter as circle 1, and centered on the topmost point of circle 1.)  This is all amazing to me but maybe not to the real mathematicians among my readers.  How can this be happening?

I should mention here that the full-size image is 1800 pixels wide and when shrunk down to fit in this column, it loses a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then on the next page, click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (this will take a few moments), and click on that to get the actual full-size. 

Something very interesting is shown in the next image.  I started putting horizontal lines through points where the orange lines intersect, still trying to find some “squares” as I mentioned in Part 1.  I found that the horizontal lines predict where a hexagram will appear in circle 2.  I’ve put in the hexagram, in red, to make it stand out.  The horizontal lines are marked with red markers.

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I copied my orange grid design, inverted, pasted, and copied, rotated 90 degrees, pasted, pivoting on the center of circle 1.  (I often manipulate designs just to see what they will do).  What a surprise!  The orange lines predict where 12-point stars will appear in the rotated green circles.  I’ve put in the 12-point stars, in red, to make them stand out.  Take a look at how the orange lines zoom through many of the points of the stars. 

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But where is the tomb symbol in all this?  Maybe I’ve drifted a bit, so I’ll bring back the “red line” derived directly from the tomb symbol in Part 1.  In the following image (shown at magnification 2X), I have many of the forms from Part 1, and thanks to my orange grid design, I could add an equilateral triangle (purple), with apex at the top point of the tomb symbol angle (pale green) and base coincident with the horizontal through the intersection of orange lines, and the base bounded by the verticals of the 12-point star.  The second equilateral triangle (“inner”) has its apex at an intersection of orange lines (inside apex of previous triangle) and its base bounded by the intersections of rotated circle 2’s.  Isn’t it neat that the triangles fit?  I also added verticals through the intersections of orange lines.  As the purple equilateral triangles and other forms are copied, flipped left/right, pasted, copied, inverted, pasted, and copied, rotated 90 degrees, pasted, they make an intricate design.  And by the way, I’ve found many equilateral triangles in my grid work here. 

Notice how the “red lines” intersect where the inner purple equilateral triangles intersect, where the verticals and horizontals intersect making the four corners of the central square.  Wow.  There are at least 8 other corners where red lines intersect outer purple triangles.  Notice how the “red lines” intersect where the outer purple triangles intersect – on the design’s axes.  Notice how the outer purple equilateral triangles intersect where the half green circles (dark green) intersect, where the “orange lines” pass through.  There seems to be a meeting of red line, inner purple triangle, green circle, and turquoise circle.  There seems to be a meeting of inner and outer purple triangles and half green circle.  There seems to be a meeting of yellow circle, green circle, and red line.  There seems to be a meeting of tomb symbol circle, yellow circle, and outer purple triangle.  It’s all so colorful and pretty. 

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Broader view

I’m wondering if the rotated outer equilateral triangle also goes through the “A point” (where “red line,” tomb symbol angle, and green circle meet).  I think maybe it does.

Well, I’m sure there is more to discover.  Continued here.

Slide show and music on my main page.

-2008-  

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

This page was updated on June 3, 2008.

DRAWING THE “JESUS TOMB” SYMBOL, PART 6

I was wondering what the tomb symbol circle did outside the environment of the circle it is derived from. 

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3,  Part 4, and Part 5.

In the following image, I have 8 “yellow circles” (75 percent of the diameter of my standard circle).  The yellow circles (deep yellow) pass through the center of the standard circle (regular blue).  I added 8 tomb symbol circles (one-fourth the diameter of the standard circle).  Each tomb symbol circle (black-green) is tangential to the standard circle and a yellow circle.  Then I added 8 half green circles.  (Previously called the “dark green circle,” it is one-half the diameter of the standard circle and one-half the diameter of the “green circle.”)  Each half green circle (dark green) is tangential to two yellow circles and a tomb symbol circle.  Then I added a half green circle centered on the standard circle.  This half green circle is tangential to the other 8 half green circles.  A row of three half royal circles (one-sixth the diameter of the standard circle) fit across the central half green circle, and I’ve added 9 to make a rosette (royal blue).

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In the following image, I added 16 half tomb symbol circles (one-eighth the diameter of the standard circle).  Each half tomb symbol circle (pink) is framed by two yellow circles and a half green circle.  Next I added a royal circle (one-third the diameter of the standard circle) centered on the standard circle.  Of course, this royal circle (royal blue) passes through the centers of the half royal circles.

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In the following image, I added 8 green circles (same diameter as the standard circle) tangential to the 8 peripheral points where the yellow circles, tomb symbol circles, and half green circles meet.  Each green circle (deep turquoise) is also tangential to the central half green circle, and appears to pass through two additional points, where half green circles are tangential to a yellow circle.  Each green circle appears to cuddle two of the 16 half tomb symbol circles, and I added 8 more half tomb symbol circles, each framed by 4 green circles.  Now each green circle cuddles 6 half tomb symbol circles.

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Continuing on my journey to build this design, I added a yellow circle centered on the standard circle.  The central yellow circle is thicker, because it is pasted four times.  A one-pixel center won’t go symmetrically on a four-pixel center unless it is pasted four times, onto each of the four pixels – the software has such peculiarities.  Once I added that central yellow circle, I could add a rosette of 8 royal circles, each tangential to 3 yellow circles (including the central yellow circle just added).  With the addition of the royals, I found a way to add 8 half tomb symbol circles within the central royal circle.  Each of these is tangential to two royal circles and possibly two yellow circles.  See the following image.

Full-size image

Does the tomb symbol circle keep on working even when outside the circle that spawned it?  Yes, indeed.  Isn’t it wonderful that all these circles fit together so nicely?  This particular design has 85 circles by my count.  Can you find them all?

On my journey, I seem to be finding all sorts of interesting things.  Continued here.

Slide show and music on my main page.

-2008-

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