Re: Zero the Hero.

On Thu, 10 Aug 2006 12:45:52 +1000, "Adam Whyte-Settlar"
<grawillers@xxxxxxxxxxx> wrote:


"Josiah Jenkins" <josiah-jenkins@xxxxxxxxxxxxx> wrote in message
news:piukd2lv4dq37sh47ee6e17m1abtgu569r@xxxxxxxxxx
On Wed, 09 Aug 2006 22:29:09 GMT, I read these words from Cory
Bhreckan <corybhreckan@xxxxxxxxxxxxx> :

<snip>

On the human front, written language was invented exactly twice as was
the mathematical concept of zero, once in the "new world" (they invented
zero first)

You got a source for that last ?
Without wading thro' the quoted URL.
(And no, I'm not extracting the urine, I'm interested)

The Mayans had some kind of place-value system which included the concept of
'zero' I believe.
However I understand the Indians (from India) claim they 'invented' it
anything up to 10,000 years ago or more despite the fact that the first
definite undisputed use of it in India was as recent as about 1,500 years
back.
The Babylonians had the 'concept' but didn't have any actual figure - the
'concept' was apparent from the 'context' of the sum - more of a punctuation
mark than a number if you follow me.

In Arabic script, zero is still written as a full stop/period.

Examples of written zero in various languages are halfway down this
page:
http://en.wikipedia.org/wiki/Hindu-Arabic_numeral_system

The Greeks (ptolemy?) stick their oar in too but seeing as they used the
length of lines to indicate number (I think) then some historians dispute
this was a 'true zero' too.
Also, it seems that 'zero' has been 'discovered' and then 'lost' several
times in various cultures as the discoverers failed to appreciate the
profound implications of their discovery at the time.
As usual with ancient historical questions like this it would appear that
the answer to the query 'Who invented zero' is 'No-one really knows'.

A W-S

I know that by Elizabethan times, various bypasses were used to
produce multiplication, but what has always puzzled me is how the
Romans coped with multiplication, yet apparently must have done so
somehow.

Russian serfs also divised a multiplication system which was still in
use in the 20th century until universal education was introduced by
the Communists. To operate it, all you have to know is how to double a
number, how to halve one, and simple addition.

For example, How to multiply 97 by 39:

97 x 39
48 x 78
24 x 156
12 x 312
6 x 624
3 x 1248
1 x 1296

Cross out all the even numbers in the left hand column and the
adjacent numbers in the right hand column.

This leaves:

97 x 39
3 x 1248
1 x 2496

Add up the remaining numbers in the right hand column:

+ 39
+ 1248
+ 2496
------
= 3783
------
---------------------------------------------------
Elizabethan multiplication is more complicated to set up, but almost
as fast as any modern method. To multiply 123 x 456:

Draw a lattice with 3 x 3 squares for a total of 9 squares and divide
each square diagonally.

-------------------
|--/--|--/--|--/--|
|--/--|--/--|--/--|
|--/--|--/--|--/--|
|--/--|--/--|--/--|
|--/--|--/--|--/--|
|--/--|--/--|--/--|
-------------------

Write one of the numbers along the top and the other down the side

1 2 3
-------------------
|--/--|--/--|--/--| 4
|--/--|--/--|--/--|
|--/--|--/--|--/--| 5
|--/--|--/--|--/--|
|--/--|--/--|--/--| 6
|--/--|--/--|--/--|
-------------------

Multiply the end digit along the top by each of the numbers in the
first column in turn. Put the units part of each answer in the bottom
part of the appropriate lattice triangle, and the tens part in the top
of each triangle.
Carry out the same process for the other two numbers along the top.

A:
-------------------
1 2 3
|--/--|--/--|1-/--| 4
|--/--|--/--|--/2-|
|--/--|--/--|1-/--| 5
|--/--|--/--|--/5-|
|--/--|--/--|1-/--| 6
|--/--|--/--|1-/-8|
-------------------

Add each column in turn, starting with the bottom right hand-column
and write down the totals along the bottom and up the left hand side
of the square. If any line totals 10 or more, write down the units
figure for that column and carry on the tens figure to the next
column:

B:
-------------------
1 2 3
|--/--|--/--|1-/--| 4
|--/4-|--/8-|--/2-|
|--/--|1-/--|1-/--| 5
| 1/--|--/0-|--/5-|
|--/--|1-/--|1 /--| 6
|--/--|--/2-|1-/-8|
-------------------

C:
-------------------
1 2 3
|--/--|--/--|1-/--| 4
|--/4-|--/8-|--/2-|
|--/--|1-/--|1-/--| 5
|--/5-|--/0-|--/5-|
|--/--|1-/--|1 /--| 6
|--/6-|--/2-|1-/-8|
-------------------

Conclusion:
-------------------
1 2 3
|--/--|--/--|1-/--| 4
|--/4-|--/8-|--/2-|
|--/--|1-/--|1-/--| 5
5 |--/5-|--/0-|--/5-|
|--/--|1-/--|1 /--| 6
6 |--/6-|--/2-|1-/-8|
---------------------
0 8 8

Simply read off the answer - 58088.

The Highlander

Faodaidh nach ionann na beachdan anns
an post seo agus beachdan a' Ghàidheil.
The views expressed in this post are
not necessarily those of The Highlander.
.

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