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6 l! M9 m: Z3 Y5 I- Q TTriangular numbers are literally triangles.
6 X* k7 S* X! _- @" b& Q/ w 理解三角形数字的三角关系
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Consider that the progression of lighting of the candles of a Menorah over time results in the same figure as the image presented by a Christmas tree, and that both of these are the essence of the Pythagorean Tetractys.
$ v5 _8 _; x: P/ B' q4 [ 犹太教举行宗教仪式的时候经常把烛台摆成不同级别的三角形态，同时三角形也是圣诞树的形态,都属于毕达哥拉期的数字理论。) w1 h2 j. [7 [& ~
The genesis of the series in Pythagorean style. is done by adding the numbers. 1 + 2 = 3. 3 + 3 = 6. 6 + 4 = 10. 10 + 5 = 15, etc. One of the examples for which you asked for explanation was:
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561 is the triangle of 33
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9 ?% V* O6 G/ s" ~ o' G8 xIf you add 1, 2, 3, 4, 5, etc. and keep a running total as explained above, when you reach the 33rd iteration (and have just added 33) your total will be 561./ S; K$ _* c' X7 J
q9 e5 K/ k/ }7 C7 i; [ AFind the triangle of 36 and compare to the weights of gold which came in to Solomon in one year. 1 Kings 10:14
0 m5 [! X# c1 p4 l( @Knowing that 561 is the triangle of 33, we have a shortcut in that we only have 3 more numbers to add.
5 S8 r* d- P7 y) D了解561是33的三角关系，我们有一个小技巧在相加大于三的数字+ _4 o$ E# Z; _/ L) S# i# f- b) D
Interestingly, just as when we divide a geometrical square with a diagonal we get two triangles, when we add two triangular numbers we get a square. For example, 6 + 10 = 16, which is the square of 4.
2 ~, B! t' X0 Y% P' S% r有趣的是当我们用对角线分切一个几何正方形，我们可以得到二个三角形,当我们相加二个三角形的数字我们可以得到一个正方形，例如6+10=16，是4的正方形2 u v8 M* S9 S% u& W0 P+ Q
4 v9 \( M, p1 E/ r, M10 is a demonstration of the extension of the One as we see that 1 + 3 + 6 = 10.3 w, [# {- J4 k t: Z0 E/ q( s6 X3 W
10是一个扩展的特例，我们可以看到1+3+6=10,(10可以不仅表示数字级别的变化，同时类似于太极中的阴阳点)
' x! k5 r, U. c. c: F# NThese two examples are most compelling as we see that by understanding this, the squares so commonly focused on can be seen in a different light.# k: P' j* m: S$ ^+ @
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Gann supposedly went to Egypt to study Fibonnaci numbers at the foot of a pyramid with a square base.7 D5 m/ k% p7 e: j2 O
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36 is one of the special cases, a number that is both triangular and square.
+ C3 t: j$ o' h/ A( ~' S36 is the square of the Sun, obviously round, and to the Egyptians, a triangle at the same time.
8 T* t6 Y' h) f5 B) ?36也是一个特例，一个数字同时是三角和正方的关系
! j8 L7 o$ Y) j! u9 {: sLet's examine the triangular numbers that lead up to 36.5 q0 a$ y' K9 s. B& h
1 3 6 10 15 21 28 360 Q4 D. Z" S8 g4 R @
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And the squares
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Only 15 and 21 add up to 36, triangles within the square.7 A8 u. |* G& f* S7 D6 p& C p& b. w# C
只有15和21相加等于36，三角存在于四方中
8 E% o7 d4 j* V! ~2 v- KThere are those who dislike esotericism because they only see their belief about what it is. For them, I offer a suggestion of a practical example.: t7 x$ G; Z A9 p0 E \- O& x
Take a look at the attached chart of GE and the marked triangular numbers. Price as of now 35.95.
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5 O4 |% y/ g( B3 m& w) D+ eNumbers aspect in the same way as do planets. How many planets? How many numbers? It could be that a belief in a difference between numbers and astrology is but a veil concealing a greater understanding.$ {3 g+ {( ^' G) v7 w
数字现象和行星的运行方式是相同的，多少个行星(9大行星)？多少个数字(1-9)?数字和星象是存在差异的，但隐藏着更深的秘密.
2 y/ T. u# w. w/ G$ h) YThat wch I have said of ye apocalypse of ye golden mean and ye one male and female god is hereby accomplished and ended. : )/ O- q" J0 t9 F) m2 J8 z; H
+ @0 m1 M- O |( a6 u( w/ q/ K[本帖最后由 mzyma1355 于 2008-7-13 22:36 编辑 ] |
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