At school, when we were taught about right-angled triangles, we were shown a diagram like this:

If we build out squares from a triangle whose sides measure 3, 4, and 5 - we can see that the two smaller areas add up to the large area (9+16 = 25), and the spotted angle of the triangle is a right angle (90 degrees).

This will work with a right-angled triangle of any dimensions and proportions, but it becomes interesting to numerologists when all three sides are made of whole numbers. It is formalised in a "rule" accredited to Pythagoras (Samos, Greece, 500+ BCE) which says "The square on the hypotenuse is equal to the sum of the squares on the other two sides."

The ancient Egyptians had been using 3-4-5 triangles in their buildings for a very long time before Pythagoras, so we should credit them with the discovery. Pythagoras certainly visited Egypt, and possibly studied there.

Meanwhile, in northern Europe, druids wore belts with twelve equally spaced knots. Some say that this represented the twelve astrological signs. However, part of a druid's job was to lay out ceremoniously the ground plan of any significant new building. Observe that the sides of our 3-4-5 triangle add up to twelve (3+4+5 = 12). So the druid used his belt like this:

...in order to make sure the new building had its walls at right-angles to each other.

For numerologists, this triangle shows us an interaction between three, four, and five - wherein the five locks the three and four in a special relationship. So the relationship between creativity (3) and stability (4) becomes special when acted upon by communication (5) or the microcosm. Out of this we also see a new function for the twelve (number of humanity). We should also note that the area of this triangle is 6 (which is the number of Love and the macrocosm) because the triangle covers half a 4x3 grid whose whole area would be twelve.

Summarising: our 3-4-5-triangle shows us 12 in its perimeter and 6 in its area.

This triangle is not unique. It is the first of many "integer" (whole number) right-angled triangles. The others will also reveal special relationships between their own numbers.

Obviously we can find many larger triangles by multiplying what we have already. So the 3-4-5 triangle also gives us

- 6-8-10 which is the 3-4-5 times 2
- 9-12-15 which is the 3-4-5 times 3
- 12-16-20 which is the 3-4-5 times 4

For completely fresh information we must look for new integer right-angled triangles which have a side which is a **prime** number. We could also look at multiples of each of these, but let us concentrate on the core triangles rather than functions of them.

- 3-4-5, perimeter 12, area 6
- 5-12-13, perimeter 30, area 30
- 7-24-25, perimeter 56, area 84
- 8-15-17, perimeter 40, area 60
- 9-40-41, perimeter 90, area 180
- 11-60-61, perimeter 132, area 330
- 12-35-37, perimeter 84, area 210
- 13-84-85, perimeter 182, area 546
- 15-112-113, perimeter 240, area 840
- 17-144-145, perimeter 306, area 1224
- 19-180-181, perimeter 380, area 1710
- 20-21-29, perimeter 70, area 210
- 20-99-101, perimeter 220, area 990
- 23-264-265, perimeter 552, area 3036
- 25-312-313, perimeter 650, area 3900
- 28-45-53, perimeter 126, area 630
- 28-195-197, perimeter 420, area 2730

The sequence continues indefinitely. This list up to 28-shortest-side may not even be complete within itself, as the search went only as far as maximum side length 3,000.

Notice the absence of 2, 6, 10, 14, 18, 22, 26... (continues in steps of 4). This sequence of absentees must tell us something about these numbers being in some way "un-triangular". That appears contradictory, as 6 and 10 (and later 66, 78, and many others) are actual triangular numbers in the mathematical sense. We should always notice the absentees from a sequence, as they form a kind of photographic negative of the sequence itself. The paradox in this instance seems to say it is especially important. It could be that they are in some way "not right-angular", but then why is the 10 there when it is the secret key to the 4? Sorry - I can't see why. Can you? Any answers to this are acknowledged as your copyright, and will remain your intellectual property.

For some of these triangles (and some of their multiples) we can look at the Aura-Soma Equilibrium Bottles to help us study (a) how the hypotenuse (longest side with the highest Bottle number) locks the relationship between the Bottles of the other two sides, then (b) look at how the bottles of the perimeter and the area relate to the Bottles of the sides.

3-4-5, perimeter 12, area 6

Some ancient Greek schools did not see 1 or 2 as numbers but rather the sources of number. So for them the 3-4-5 is made of the first three perceived numbers, giving it more importance.

5-12-13, perimeter 30, area 30

The Sun is associated with 12 because of the zodiac signs. The Moon has 13 cycles in a year. The 5 is the number of the microcosm man. So it seems important here to concentrate on the relationship between the Moon, the Sun, and the human - rather than any other attributes or associations of these numbers. This seems to take us back to the druids again, as the Moon was the source of light which helped the hunter find food, but the Sun became more important to the later farmer. Note that this is the **only** case of the perimeter being the same number as the area.

7-24-25, perimeter 56, area 84

The "Innermost" (25) part of us helps to see a relationship between the Triumph of Spirit over Matter (7) and the Leaders of the Tribes (24) (male and female archetypes of the twelve zodiac signs), within a perimeter of rôle reversal between macrocosm and microcosm, in an area of stability within the spiritual Law.

8-15-17, perimeter 40, area 60

The Law (8), and Discernment (16), are held together by The Star (17). So the guidance from above helps us to reach a discerning understanding of the laws of the spiritual universe. The perimeter of 40 (Endurance) suggests that this may take us some time and determination. The area is 60, is a meditation on the 6, and 6 is the number of Love and the macrocosm. The 60 is also significantly 3x4x5, so an intense relationship between Creativity, Stability, and Communication - and 3-4-5 is where we started all this.

Any triangle is an expression of the three, so a function of creativity. The three is the union of the one and the two. In the case of right-angled triangles, the one's function is manifest in the longest side (hypotenuse) and the two's function is expressed in the two shorter sides. So we work in an awareness of the original function of the one and the two.

If you would like to ask a question about this article, please email john@dillon-guy.com

In article 2 on "The Basics" the question was asked "Do you have any suggestions for well known characters in fiction or history who could be seen as archetypical of one of the single digits?"

"9 = Frodo from Lord of the Rings by Tolkien.

Selflessness, implying personal sacrifice, Frodo left his home and his life to serve a greater cause. Compassion, for his friends, and pity for Smeagol. Letting-go, of his home, his prior life and the chance for things to return to normality when he took charge of the One Ring and was wounded by a Ringwraithe. Inner-strength, to carry the One Ring which was a heavy, heavy burden."

Sharyn's insight is brilliant - real gold-dust. It really shows us how it feels to be influenced by the best personal and mission aspects of the nine. It is interesting that "Frodo Baggins" evaluates to 63 in modern numerology, so it reduces to nine.

In article 4 on "Enhancing a four bottle reading with numerology" the question was asked "What do you feel about the ethical aspects of digging for extra information which the client has not chosen to reveal overtly?"

"I would only use these techniques for clients who are familiar with Aura-Soma, numerology, tarot etc. I feel that there is usually enough information within the four bottle selection without looking for extra bottles that may be connected. The symbology may be relevant but the bottle itself has not been chosen so should not be brought out as this is not honouring the clients soul choice.

"Years ago, before learning Aura-Soma myself I had two consultations and left each consultation with a bottle to use that was not in my selection. I was aware that these bottles had been selected by adding up the primary colours and finding the most relevant bottle to make up what I was lacking. The bottle was then added to my selection to show a balanced colour choice. They were not bottles that I would have chosen!

"These bottles did have a positive effect on me and helped me a lot, but I now wonder what would have been the outcome if I had used the therapeutic bottle from my selection."

The article did say "Please never lay out any extra bottles during a reading for a normal client. It would cause them serious confusion." ...but Sharyn makes the point more powerfully. Thanks Sharyn.