Pyramiding Dots is a Mathematical Marvel.
A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right. The nth triangular number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers (sequence A000217 in the OEIS), starting at the 0th triangular number, is
- 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666…
The numerical sequence of the vertical rows on the periodic chart was coded longer than 10,000 years ago. It appears in graph form on the simplest of number squares.
Now, let ‘s look at the grid lines of the 3 x 3 number square. Look at the whole line segments. Two units are found most easily. Just look at two consecutive sides on the perimeter on the grid. We immediately found 2 units. Numbers 8, 18 and 32 are more difficult. They come as square roots of defined whole line segments on the grid
- The diagonal from points “A” to “E” (where the two dark intersect to form the right angle) This diagonal equals √8 in terms of the basic grid unit.
- Line BD (the entire diagonal of the complete square) equals √18
- Finally triangle ABD or CBD equals √32.
The numbers of the graph of the magic square as illustrated above and vertical rows of the periodic chart then become the same: 2, 8, 18, and 32.
How Pyramiding Dots is a Mathematical Marvel
Finally, regard the above number sequence of dots. Again, look at the numbers above.
- Pyramid dots from 1 to 18. We have 153 dots.
- Pyramid dots from 1 to 32. We have 496 dots.
Key vertical coding numbers on the periodic chart can appear when we use the pyramided form of dots aw 18 and 32. All posts on DSOworks.com are free. For those who have read them, 18 and 32 also are key numbers of the five Platonic solids. Three of the solids total 32 triangulated faces. The other two total 18 non-triangulated faces.
Final Point With Pyramiding Dots
Look at the totals for the 18 and 32 rows. They total 153 and 496 respectively. These are key numbers in Christianity and mystical Judaism.
- “Simon Peter climbed back into the boat and dragged the net ashore. It was full of 153 large fish, but even with so many the net was not torn”. This has become known popularly as the “153 fish” miracle. Gospel of John, seven of the disciples—Peter, Thomas, Nathanael, the sons of Zebedee (James and John), and two others – decided to go fishing one evening…
- Malkuth, Malchut or Malchus (/mɑːlˈkuːθ/; Hebrew: ملكوت ;מלכות [malˈχuːt], “kingdom”), or Shekhinah, is the tenth of the sephirot in the Kabbalistic Tree of Life. It sits at the bottom of the Tree, below Yesod. This sephirah has as a symbol the Bride which relates to the sphere of Tipheret, symbolized by the Bridegroom.
In Hebrew letters and numbers share the same symbol. The total of its 5 letters in Hebrew that spell Malkuth is 496. The number 496 is one of the pyramided totals of dots given above.
Conclusion: Somehow and sometime, perhaps with the Great Flood, an entire civilization was destroyed. Those on Noah’s Arc survived. We have struggled by our collective sweat of our brow ever since. I believe the tiny 3 x 3 number square holds the key to a lost and prehistoric Golden Age. In reviving this “Grain of Mustard Seed” we have the tool we need to create another Golden Age of peace and plenty.