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Triangular numbers are literally triangles.
: x9 f& F1 v _8 M: z* I* a0 Y 理解三角形数字的三角关系
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& r0 r& n/ p# d0 mConsider 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.
: s- _1 C: l4 G7 c4 | 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。3 ^" g u3 ]# `
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:* ~5 @+ o9 o/ S) n6 t+ C
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561 is the triangle of 33
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If 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.
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; L9 ?2 {- G6 h- G, E% |# P4 t3 qFind the triangle of 36 and compare to the weights of gold which came in to Solomon in one year. 1 Kings 10:14
! O& k# G' a+ a# i! f5 s! aKnowing that 561 is the triangle of 33, we have a shortcut in that we only have 3 more numbers to add.
' m. Y- @: i( ?" Q2 L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3 U$ w6 t c2 |/ V0 P7 r2 s
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.' Z+ o+ o1 }* z6 ]
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
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2 n3 E+ @- N( f* X10 is a demonstration of the extension of the One as we see that 1 + 3 + 6 = 10.
5 ?4 Y* R( R. Q+ {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)
, @' h# y* V8 _$ q5 C( UThese 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.$ v! f" ?$ G1 d& A! _
5 U* P4 _! y* N# u& C: |% r( DGann supposedly went to Egypt to study Fibonnaci numbers at the foot of a pyramid with a square base.
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1 Q6 X# L9 M8 w( P) ~36 is one of the special cases, a number that is both triangular and square.
" q! x$ `% T& |+ E H4 N0 s- r36 is the square of the Sun, obviously round, and to the Egyptians, a triangle at the same time.
# N( @. r2 d& w36也是一个特例,一个数字同时是三角和正方的关系, L+ i# P2 v6 K4 V7 s
Let's examine the triangular numbers that lead up to 36.
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Only 15 and 21 add up to 36, triangles within the square.! n* `4 l' \& A5 D/ c" S6 Z+ \
只有15和21相加等于36,三角存在于四方中
. }1 `1 X3 ]& Z0 L) z, `There 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.
; ] S5 }# b G Y2 J% {) ^Take a look at the attached chart of GE and the marked triangular numbers. Price as of now 35.95." f* U6 e2 O5 q: i+ r, @
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Numbers 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.& Z1 t& z7 }+ Z1 e4 F9 x
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.
9 o0 F8 D* g2 sThat wch I have said of ye apocalypse of ye golden mean and ye one male and female god is hereby accomplished and ended. : )2 `9 g! V) P& L! X$ g' i% M0 _1 M
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[本帖最后由 mzyma1355 于 2008-7-13 22:36 编辑 ] |