| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
2 2 2
We all know that 3 + 4 = 5 .
3 3 3 3
Did you know that also 3 + 4 + 5 = 6 ?
Any other "funny" combinations like this? Any special reason for this?
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 330.1 | METOO::YARBROUGH | Thu Aug 29 1985 10:24 | 22 | ||
This is a special case of the identity
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
a (a +b ) = b (a +b ) + a (a -2b ) + b (2a -b )
3
for a = 2, b = 1 (divide the result by 3 ).
A similar identity is:
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
a (a +2b ) = a (a -b ) + b (a -b ) + b (2a +b )
I like the following relationship:
n n n n n n n n n n n n n n n n
1 +13 +28 +70 +82 +124 +139 +151 = 4 +7 +34 +61 +91 +118 +145 +148
for n = 1...7
All of this is from "Recreations in the Theory of Numbers" by A. H. Beiler,
published by Dover in 1964. Great book for people like us.
Lynn Yarbrough
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| 330.2 | ADVAX::J_ROTH | Thu Aug 29 1985 17:50 | 9 | ||
I was about to post a similar reply... I had Beiler for freshman caclulus in 1967, he was an interesting character; I didn't find out about his book until quite a bit later though. I don't know if he's still living, he was quite old at the time. - Jim | |||||