Please ignore the first 2 posts that the values in the root brackets were missing.
Sorry for the multiple posts.
We will continue from the last post, we already established the vectors for triangle DEF
in the previous analysis as
Cycle DEF:
Vector DE = root(498² + 438.32²) = 663 units
DE is the base of triangle DEF and is 1.667 expansion of the first base BC
394 x 1.667 = 657 units (short of 6 units)
Vector DF = root(1968² + 2005²) = 2809 units
Vector EF = root(1507² + 2405.94²) = 2839 units
DF and EF are also two sides of equal length and the base length DE as 663 units.
Vector FG is the correction after the completion of the 2nd growth and also forms
the base for the next triangle
FG = root(1385.69² + 18²) = 1385.81 units
Now we can see that the 3 triangle bases show successive growth
Base 1 = BC = 394 units
Base 2 = DE = 663 units (394 x 1.667 = 657, that is 1.667 expansion of BC)
Base 3 = FG = 1386 units (663 x 2.09 = 1386, that is also 2.0 expansion of DE)
Also the ratio of base to side for each successive triangle shows a growth pattern
For triangle ABC, base to side = 1 : 3
Base BC = 394
Sides AB = 1103.36, and AC = 1140.35
394 x 2.9 = 1142 ( Approx. 1 : 3)
Triangle DEF, base to sides = 1 : 4.236
Base DE = 663
Sides DF = 2809 and EF = 2839
663 x 4.236 = 2809 ( ratio = 1 : 4.236)
Now the 3rd base FG which is 2.0 expansion of 663 has completed but the
sides GH and GI/FH are yet to form in time.
Our projections are that if the growth process continues then we can expect
sides GH and GI/FH to be 5 times the value of the base vector AC or AB to maintain
the 1,1,2,3,5,8... Fibonacci series
AC = 1140
5 x 1140 = 5700 units (for GH and GI/FH)
The ratio of Base to sides must also be maintained at 1 : 4.236 to match
the vector expansion. ( Preferably 1 : 4.142)
Triangle base = FG = 1386 units
1386 x 4.142 = 5741 ( approx = GH =5700)
(The value 4.142 would be explained in next post)
Please check next post for continuation... thanks
Sorry for the multiple posts.
We will continue from the last post, we already established the vectors for triangle DEF
in the previous analysis as
Cycle DEF:
Vector DE = root(498² + 438.32²) = 663 units
DE is the base of triangle DEF and is 1.667 expansion of the first base BC
394 x 1.667 = 657 units (short of 6 units)
Vector DF = root(1968² + 2005²) = 2809 units
Vector EF = root(1507² + 2405.94²) = 2839 units
DF and EF are also two sides of equal length and the base length DE as 663 units.
Vector FG is the correction after the completion of the 2nd growth and also forms
the base for the next triangle
FG = root(1385.69² + 18²) = 1385.81 units
Now we can see that the 3 triangle bases show successive growth
Base 1 = BC = 394 units
Base 2 = DE = 663 units (394 x 1.667 = 657, that is 1.667 expansion of BC)
Base 3 = FG = 1386 units (663 x 2.09 = 1386, that is also 2.0 expansion of DE)
Also the ratio of base to side for each successive triangle shows a growth pattern
For triangle ABC, base to side = 1 : 3
Base BC = 394
Sides AB = 1103.36, and AC = 1140.35
394 x 2.9 = 1142 ( Approx. 1 : 3)
Triangle DEF, base to sides = 1 : 4.236
Base DE = 663
Sides DF = 2809 and EF = 2839
663 x 4.236 = 2809 ( ratio = 1 : 4.236)
Now the 3rd base FG which is 2.0 expansion of 663 has completed but the
sides GH and GI/FH are yet to form in time.
Our projections are that if the growth process continues then we can expect
sides GH and GI/FH to be 5 times the value of the base vector AC or AB to maintain
the 1,1,2,3,5,8... Fibonacci series
AC = 1140
5 x 1140 = 5700 units (for GH and GI/FH)
The ratio of Base to sides must also be maintained at 1 : 4.236 to match
the vector expansion. ( Preferably 1 : 4.142)
Triangle base = FG = 1386 units
1386 x 4.142 = 5741 ( approx = GH =5700)
(The value 4.142 would be explained in next post)
Please check next post for continuation... thanks
On the chart the values for DF and EF were interchanged but it doesn't affect the analysis, thanks for the correction buddy.
DF = 1968 points
2005 days
EF= 2405.94 points
1507 days