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Topic: RMP # 48
Replies: 70   Last Post: Jul 23, 2010 8:57 AM

 Messages: [ Previous | Next ]
 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Re: RMP # 48
Posted: Oct 7, 2007 8:48 AM

Milo, the false additions have nothing to do with false propositions.
They are a means of getting good values from a poor and a mediocre
one, or an excellent value from a mediocre and a good one. Take
for example the square root of 17. It is less than 5 but a little more
than 4. Now form the fractions 5/1 and 4/1. Adding them correctly
yields 9/1 or 9. Adding them in the 'forbidden' way yields 5 plus 4
divided by 1 plus 1, or 9/2. Begin a sequence of false additions with
5/1 and add repeatedly 4/1:

5/1 (plus 4/1) 9/2 13/3 17/4 21/5 25/6 29/7 33/8 37/9 ...

33/8 or 4 '4 is a good value for the square root of 17, as the
squared fraction yields 17 '64. Now begin a second sequence
of false additions with the mediocre value 4/1 (too small)
and add repeatedly the good value 33/8 (slightly too big):

4/1 (plus 33/8) 37/9 70/17 103/25 136/33 169/41 202/49
235/57 268/65 301/73 ...

This sequence contains a lot of very good values, and you can
choose the one that fits handily into a given calculation.

Regards, Franz Gnaedinger

Date Subject Author
9/30/07 L. Cooper
10/1/07 Franz Gnaedinger
10/1/07 L. Cooper
10/1/07 Milo Gardner
10/1/07 L. Cooper
10/2/07 Milo Gardner
10/3/07 Milo Gardner
10/3/07 L. Cooper
10/3/07 Franz Gnaedinger
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 L. Cooper
10/5/07 L. Cooper
10/5/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/9/07 Franz Gnaedinger
10/9/07 L. Cooper
10/10/07 Franz Gnaedinger
10/11/07 Franz Gnaedinger
10/11/07 L. Cooper
10/12/07 Franz Gnaedinger
10/12/07 Franz Gnaedinger
10/12/07 L. Cooper
10/13/07 Franz Gnaedinger
10/13/07 L. Cooper
10/13/07 Franz Gnaedinger
10/15/07 Franz Gnaedinger
10/18/07 Ed Wall
10/19/07 Franz Gnaedinger
10/20/07 Milo Gardner
12/5/07 Milo Gardner
12/14/07 Franz Gnaedinger
12/14/07 Milo Gardner
12/14/07 Milo Gardner
10/11/07 Milo Gardner
10/12/07 L. Cooper
10/12/07 Milo Gardner
10/13/07 L. Cooper
7/11/10 Dioxippus
7/12/10 Milo Gardner
7/20/10 Dioxippus
7/21/10 Milo Gardner
7/21/10 Dioxippus
7/21/10 Milo Gardner
7/23/10 Dioxippus
7/23/10 Milo Gardner
10/6/07 Hossam Aboulfotouh
10/8/07 Milo Gardner
10/11/07 Hossam Aboulfotouh
10/12/07 Milo Gardner
10/13/07 Hossam Aboulfotouh
10/13/07 Hossam Aboulfotouh
10/19/07 Hossam Aboulfotouh
10/27/07 Matt Hugh