Paul Moosberg
Five Grouped Cubes  Poem by Paul Moosberg
The last and vast digits of change start to run
In groups it loops seven nine seven one one
The nines can shine that an off pattern is spun
In groups of troops between nine and seven’s son
Then cube the tube if X has seven or two
Inside to hide X’s last digit’s value
Then count amount to times as the five’s debut
Inside this stride minus six from five to view
A two to do as X N as one to state
Loop (Next of X) cube minus X cube plus fate
One fifty lifted by N to show its trait
Cube on (six) dawn (five) then X and N update
Declare:
X=2, N=1
Loop:
(X+1) ^3  X^3 + 150N = (X+6) ^3  (X+5) ^3
X=X+5
N=N+1
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Yes, I'm getting there now, Paul. I understand it up to the halfway point. I'll crack it eventually. Like you, I just love numbers  they are fascinating. I will keep coming back and back.........
Love, Fran xx (Report) Reply
the trick is this:
1^3=1,2^3=8,3^3=27,4^3=64,5^3=125,6^3=216,7^3=343,8^3=512,9^3=729,10^3=1000,11^3=1331
now if you take the difference of the adjacent (next to eah other) cubes then there is a pattern in that last digit of the difference between. the pattern is 79711 so it is a group of five differences that repeats and always does 79711 as the last digit of the answer. ie the differences from example above:
7,19,37,61,91,127,169,217,271,331
see last digits are 79711 repeating
well the cubes that make the pattern of the last digits as 9 can caculate a later power of +6 to the lower of the 2 cubes that are adjacent in the examples at the top. but funny enough the cubes that are producing the difference with a last digit of 9 are ending in 2 or 7 since the grouping of this pattern 79711 is a group of five.
then i put the counter in to show the derivations or what ever, but the difference of the difference ups by 150 evey 5 cubes so this gave me a way to calculate what the 2nd or the 3rd in the next group by flopping the opposing to the other side of the equal sign with some different math to them. but the basis is that i can calculate the numbers cubed if the numbers being cubed end in 2 or 7.
it's kinda funny that it works cause it is really wierd to see it in my head like spinning spirals of math and color. (Report) Reply
Hell, it's a long time since I had to use algebra (and a long time since I worked in the electronics business) . I tried to understand this but just couldn't. My mind is all scrambled up now............but thanks for a poem that really got me thinking.
Love, Fran xx (Report) Reply