## 2394Re: Pythagorean triples/area-perimeter relations

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• Aug 1, 2001
In message <cb.1443eee7.2899075a@...>, mikebispham@... writes
>Hi Neil
>
>Re the area/dia business - of course its obvious when you see them as
>decimals. We're looking at whole number right-angle triangles, pairs of
>which will fit together to make whole number rectangles, so of course both
>diameters and areas will be either whole or whole and a half!

I am missing something here. The hypotenuse will be an integer, the area
will either be an integer or end in .5, but why does area/perimeter have
to be an integer or end in .5?

>calculates them? I can do radians but not sine etc on my spreadsheet, and I
>don't know how to work radians for trigonometrical purposes.

This is all in the spreadsheet I'm trying to post. The formula for
conversion from degrees to radians is R = (pi/180) * D where R is the
angle size in radians and D is the angle size in degrees. The
spreadsheet calculates the angles using the formulae ASIN(B109/D109)
where B109 contains the shortest side and D109 contains the hypotenuse,
and ASIN(C109/D109) where C109 contains the middle side. The ASIN

>> Here is the full list of available 'Save As...' options in Excel 97 (aka
>> Excel 8).
>>
>> xls
>> wks
>> xlt
>> prn
>> txt
>> csv
>> xlw
>> wk4
>> wk3
>> wk1
>> wq1
>> dbf
>> dif
>> slk
>> xla
>> (html)
>>
>This opened ok, but I only have numbers, not calculation. Is that right?

No, it should be the whole thing.

>But...
>
>> I've saved it as csv (comma separated variables), attached below, hoping
>> this works. If this is the generic format we can all use, this will be
>> great, the file is only 16kB in size. Not sure what 'ss' is - is it the
>> 'generic' spreadsheet format used by Works?
>
>I can't save as csv. My options are:
>
>works ss
>works for windows 3.0 ss
>works for windows 2.0/works for dos ss
>text & commas

'text & commas' may be the same thing as csv, not sure.

>text & tabs
>text & tabs(dos)
>excel ss
>lotus 1-2-3
>works 3.0 for macintosh ss (*.ss)
>works 4.0 for macintosh ss (*.ss)
>
>I've attached a 'text & commas' file (which saves as csv - loses 'special
>formatting' - bold, italic, don't know what else, but at least we can still
>open it. Does this work for you?

Couldn't find the file.

>I've added columns to the triples for:
>
>AREA
>SUM (perimeter)
>
>I can see some interesting and resonant numbers emerging, which might attach
>particular significance to those triples that generate them - especially in
>the sexagisimal framework. So far my favourite is:
>
>18 24 30 216 72
>
>A very sixy number!

:-)

In message <LAW2-F53e1GTtBXO84t0001057a@...>, Terrie Halprin
<thalprin@...> writes

<snip>

>Neil, I am taking a look at these grids, the micro and macro in context,
>this morning AND I notice that these 14 prime triples, originally listed
>in/as micro prime, in the macro grid, have two more triples added to them:
>48 55 73 and 65 72 97 and that the 12 35 37 hasn't been pulled to
>the side -Ooh- so, you can in fact get to the 16/ square -man, that is just
>so FANTASTIC!

Terrie, thanks for this correction. Interesting that 16 appears in this
way when one works with a maximum side length of 100, another square.

I was going to post something about how area/perimeter doesn't give what
modern science would call a pure number, since according to modern
science it would have dimensions of length, since area has dimensions of
length squared, and perimeter has dimensions of length. IMO modern
science has got something wrong with regard to dimensions. It seems so
weird and maybe even 'arbitrary', for example, that a given physical
constant has, say, dimensions of mass squared times length times time.
Doesn't sound convincing. Too far away from the Pythagorean view of
numbers as basic. But unfortunately I have not reached the stage of
formulating a coherent alternative viewpoint! Very interesting, how the
discussion is going with regard to the relationship between area and
perimeter, expressed as a number.

We are going away for a week.

Best regards,

Neil
--
Neil Fernandez
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