"Mark Hopkins" <[email protected]> wrote in message
news:[email protected]...
> My, My....thats an awfully big pi...
Pi are not square. Pi are round. Cake are square.
Is this the world's oldest math joke?
Bob
"Morris Dovey" <[email protected]> wrote in message >
> C = ? · D
> = ? · 32.5
> = 102.10176124166828025003590995658 [approximately]
>
> --
> Morris Dovey
> DeSoto, Iowa USA
>
Ya, but my ruler is not able to read that close. Why not just round it off
to a more realistic number like 102.10176124166828?
On Tue, 24 Aug 2004 15:10:46 -0400, Ken McIsaac <[email protected]>
wrote:
>The trick is the "at most". I just wanted flat at both ends and the
>curve in between equally distributed. At the risk of dwelling on it:
>f(x)=6x^5 - 15x^4 + 10x^3 between x=0 and x=1 is the function I
>settled on.
Neat!!
>It's not as strange as all that, and I probably could have achieved
>the same thing with a set of french splines. This way, I got to tell
>myself I was "woodworking" when what I was actually doing was
>playing with Matlab. I got to have similar fun when I sat down to
>plan the angle I needed to cut a desired cove on my table saw. As
>always, the doing was much harder than the math.
I use Mupad for something more dramatic, but will stick to simpler
programs, usually preferring to figure by hand. My brother in law was
a draftsman, and left me some of his tools. One "French curve" is in
the shape of a babe. I'm afraid to handle her too much ...too
distracting, so she sits in a drawer.
>I did find myself a cheap (free) CAD package, but I found it very hard
>to use. My (minimal) CAD training is 15 years old, and at that time,
>you typed in the coordinates of the points you wanted and the machine
>drew it for you. These days, apparently, it's all about starting with
>blank shapes and doing cutting planes or rotations on them. This is
>not how my brain works at all.
Do try Deltacad. It's very intuitive. All have a learning curve, but
this one is relatively slight. Recently I drew up a model of our
front door that I have to rebuild. Just rectangles and a few lines
and dimensions are figured automatically. The end product is
infinitely neater than I could draw or sketch.
Bill.
On Mon, 23 Aug 2004 19:29:09 -0400, Bill Rogers <[email protected]>
wrote:
>On Mon, 23 Aug 2004 16:47:43 -0400, Ken McIsaac <[email protected]>
>wrote:
>
>> I
>>actually computed a fifth order polynomial approximation to the chair
>>leg curve I wanted on a table I made for my mother-in-law last year.
>
>That one I'd like to see.
>
I knew the shape I wanted, but I can't draw (as you say, stick people
are also beyond me), so the only way I could represent it was
mathematically. I wanted the leg to be two inches wide at the top,
one inch wide at the bottom and one-and-a-half-inch wide halfway down.
I also knew I wanted the first derivative to be zero at the top and at
the bottom, and I wanted the second derivative to be zero halfway
down. That's enough to define a fifth order polynomial. The fun part
was going to be to try to do it on two faces of the leg to get the
three-dimensional shape I wanted.
So I got out Matlab and plotted the thing, then I tried to draw it on
the leg with a pencil. Then I contemplated actually cutting it with
my crappy jigsaw. Then I decided my mother in law would be very happy
with a tapered leg. :)
>Then your own designs are fairly simple.
It's not quite that my designs are simple. It's just that I have to
take my original crazy designs and simplify them until they contain no
parts that I can't make. Right now, that means it has to require no
skill. I need a fence or guide or something to follow or the results
are not pretty. I understand from my reading that people typically
cut curves by following a hardboard template. I'm not sure how this
solves the problem, since you first have to get the template right.
I have also learned that two or three hours with coarse sandpaper can
make anything look good. :)
On Thu, 19 Aug 2004 12:31:22 -0600, "Jay Windley"
<[email protected]> wrote:
>
>"U-CDK_CHARLES\Charles" <"Charles Krug"@cdksystems.com> wrote in message
>news:j_5Vc.15253$Zh3.2575@trndny02...
>| On Wed, 18 Aug 2004 12:19:27 -0600, Jay Windley <[email protected]>
>wrote:
>|
>| There are other methods, using other tools, but a carpenter's square is
>| probably the easiest to prove correct.
>
>Hence the original masons used three tools: the straightedge, the compass,
>and the square. It's amazing what you can do with those tools and a little
>"secret" geometretic knowledge.
>
I'm still a neophyte, but I'm increasingly reaching the conclusion
that a little geometric knowledge is all you *want* to have. Because
of a misspent youth, I can do a lot of what people tell me is fairly
complex mathematics in my head. So I wind up designing furniture that
contains 18.7457 degree angles, or better yet, angles that are
arctan(5.75/11) or lengths that are (5+sqrt(7))/2 or something. I
actually computed a fifth order polynomial approximation to the chair
leg curve I wanted on a table I made for my mother-in-law last year.
Unfortunately, I have learned that I can do the math, but I can not
cut these crazy dimensions accurately. From now on, it's 90 degrees
or 45 degrees or re-design it because it's wrong.
>-- Jay
"Bob Schmall" <[email protected]> wrote in message
news:[email protected]...
>
> "David F. Eisan" <[email protected]> wrote in message
> news:[email protected]...
> > See a Rabbi.
> >
> > Oh, that's something else, nevermind...
>
> How long is a mohel?
Not sure, but I know I'm short about 4 or 5 inches. I guess they used me as
an organ donor.
moyo wrote:
> knowing that the diameter of a circle is 32 and 1/2 inches, How do I
> figure the outside length of the disk.
>
> TIA
>
> moyo
( п = 3.1415926535897932384626433832795 [approximately])
C = п · D
= п · 32.5
= 102.10176124166828025003590995658 [approximately]
--
Morris Dovey
DeSoto, Iowa USA
On Tue, 24 Aug 2004 13:16:22 -0400, Bill Rogers <[email protected]>
wrote:
>I won't dwell on it, but you still lose me. A 5th degree polynomial
>has [at most] four local max/min; i.e. the plot goes
>up/down/up/down/up. That's a strange shape for a leg. :-)
The trick is the "at most". I just wanted flat at both ends and the
curve in between equally distributed. At the risk of dwelling on it:
f(x)=6x^5 - 15x^4 + 10x^3 between x=0 and x=1 is the function I
settled on. I think it'sa fairly standard chair leg shape, actually,
although I don't know the name of it. The up/down/up/down/up
part happens outside the range of interest.
It's not as strange as all that, and I probably could have achieved
the same thing with a set of french splines. This way, I got to tell
myself I was "woodworking" when what I was actually doing was
playing with Matlab. I got to have similar fun when I sat down to
plan the angle I needed to cut a desired cove on my table saw. As
always, the doing was much harder than the math.
>I find DeltaCad really helpful. A bit of a learning curve for a
>drawing klutz like myself, but I finally got the hang of doing spline
>curves.
I did find myself a cheap (free) CAD package, but I found it very hard
to use. My (minimal) CAD training is 15 years old, and at that time,
you typed in the coordinates of the points you wanted and the machine
drew it for you. These days, apparently, it's all about starting with
blank shapes and doing cutting planes or rotations on them. This is
not how my brain works at all.
>
>Bill.
Ken McIsaac wrote:
> It's not quite that my designs are simple. It's just that I have to
> take my original crazy designs and simplify them until they contain no
> parts that I can't make. Right now, that means it has to require no
> skill. I need a fence or guide or something to follow or the results
> are not pretty. I understand from my reading that people typically
> cut curves by following a hardboard template. I'm not sure how this
> solves the problem, since you first have to get the template right.
Plot your design. You can either superimpose it on a grid and
scale it; or you can find a way to plot it full size. If
necessary run it out on your printer in pieces, one piece per
page, and then tape the printed pieces together...
Now you can transfer the design to the hardboard. Did you know
that you can get hardboard with a slick white surface at the
lumberyard?) I have a piece tacked to the wall that I sketch on
with dry erase markers - lets me re-draw to my heart's content.
Practise makes (more) perfect. (-:
--
Morris Dovey
DeSoto, Iowa USA
Ken McIsaac wrote:
> Unfortunately, I have learned that I can do the math, but I can not
> cut these crazy dimensions accurately. From now on, it's 90 degrees
> or 45 degrees or re-design it because it's wrong.
I had the same problem. You can solve (most) such problems with a
CNC router; but it's a tad spendy if you're not serious about
making it pay its own way.
--
Morris Dovey
DeSoto, Iowa USA
loutent wrote:
> Now if you live in Indiana, you can simplify your Pi
> calculations.
>
> If you've never heard this story, it's an interesting read:
>
> http://www.agecon.purdue.edu/crd/Localgov/Second%20Level%20pages/Indiana
> _Pi_Story.htm
Lou...
Interesting read. About that same time there were a number of
states who considered similar legislation; and (I've heard but
haven't confirmed) at least one state who actually enacted a
statute defining pi to be exactly three.
--
Morris Dovey
DeSoto, Iowa USA
"David F. Eisan" <[email protected]> wrote in message
news:[email protected]...
> See a Rabbi.
>
> Oh, that's something else, nevermind...
How long is a mohel?
Edwin Pawlowski wrote:
> "Morris Dovey" <[email protected]> wrote in message >
>
>> C = ? · D = ? · 32.5 = 102.10176124166828025003590995658
>> [approximately]
>
> Ya, but my ruler is not able to read that close. Why not just
> round it off to a more realistic number like
> 102.10176124166828?
Can if you want to - but I have standards to maintain!
Just imagine the horrible consequences of an only
0.00000000000000025003590995658" gap in a tinfoil helmet...
--
Morris Dovey
DeSoto, Iowa USA
On Mon, 16 Aug 2004 20:24:10 -0500, Australopithecus scobis
<[email protected]> wrote:
> Pi times the diameter. Two times pi times the radius. Pi is 3.141592654
>(Pi has infinite digits beyond the decimal, but your calculator doesn't
>care.)
>
>102.1 inches.
102 3/32 for those without decimal rulers.
Bill.
On Tue, 17 Aug 2004 11:11:27 GMT, "David F. Eisan"
<[email protected]> vaguely proposed a theory
......and in reply I say!:
remove ns from my header address to reply via email
There is a fate that shapes our ends, rough hew them though we
may.....
>See a Rabbi.
>
>Oh, that's something else, nevermind...
You use the term "figure" very well, m'sieur.
*****************************************************
Marriage. Where two people decide to get together so
that neither of them can do what they want to because
of the other one.
"Morris Dovey" <[email protected]> wrote in message
news:[email protected]...
|
| and (I've heard but haven't confirmed) at least one state who
| actually enacted a statute defining pi to be exactly three.
Tennessee, and only in Robert Heinlein's "Stranger in a Strange Land." It
didn't actually happen. The Indiana story is true enough, but it has
spawned numerous spurious copycat stories that are standard April Fool's Day
fare. Heinlein's is just the most immediately credible. The state in
question is always some state presumed inhabited by rustics. But no state
in the U.S. has ever had a law passed legislating the value of pi. Indiana
came close.
--Jay
"U-CDK_CHARLES\Charles" <"Charles Krug"@cdksystems.com> wrote in message
news:j_5Vc.15253$Zh3.2575@trndny02...
| On Wed, 18 Aug 2004 12:19:27 -0600, Jay Windley <[email protected]>
wrote:
|
| There are other methods, using other tools, but a carpenter's square is
| probably the easiest to prove correct.
Hence the original masons used three tools: the straightedge, the compass,
and the square. It's amazing what you can do with those tools and a little
"secret" geometretic knowledge.
-- Jay
On Tue, 24 Aug 2004 11:26:03 -0400, Ken McIsaac <[email protected]>
wrote:
>>>actually computed a fifth order polynomial approximation to the chair
>>>leg curve I wanted on a table I made for my mother-in-law last year.
>>
>>That one I'd like to see.
>>
>I knew the shape I wanted, but I can't draw (as you say, stick people
>are also beyond me), so the only way I could represent it was
>mathematically. I wanted the leg to be two inches wide at the top,
>one inch wide at the bottom and one-and-a-half-inch wide halfway down.
>I also knew I wanted the first derivative to be zero at the top and at
>the bottom, and I wanted the second derivative to be zero halfway
>down. That's enough to define a fifth order polynomial. The fun part
>was going to be to try to do it on two faces of the leg to get the
>three-dimensional shape I wanted.
I won't dwell on it, but you still lose me. A 5th degree polynomial
has [at most] four local max/min; i.e. the plot goes
up/down/up/down/up. That's a strange shape for a leg. :-)
>So I got out Matlab and plotted the thing, then I tried to draw it on
>the leg with a pencil.
Matlab is a bit hefty for that sort of thing. Try Graphmatica for 2D
plots: www,archives.math.utk.edu.
I find DeltaCad really helpful. A bit of a learning curve for a
drawing klutz like myself, but I finally got the hang of doing spline
curves.
Bill.
Jay Windley wrote:
>
> Tennessee, and only in Robert Heinlein's "Stranger in a
> Strange Land." It didn't actually happen. The Indiana story
> is true enough, but it has spawned numerous spurious copycat
> stories that are standard April Fool's Day fare. Heinlein's
> is just the most immediately credible. The state in question
> is always some state presumed inhabited by rustics. But no
> state in the U.S. has ever had a law passed legislating the
> value of pi. Indiana came close.
Whew! That's definitely reassuring. (-:
--
Morris Dovey
DeSoto, Iowa USA
On Wed, 18 Aug 2004 12:19:27 -0600, Jay Windley <[email protected]> wrote:
>
> "Morris Dovey" <[email protected]> wrote in message
> news:[email protected]...
>|
>| and (I've heard but haven't confirmed) at least one state who
>| actually enacted a statute defining pi to be exactly three.
>
> Tennessee, and only in Robert Heinlein's "Stranger in a Strange Land." It
> didn't actually happen. The Indiana story is true enough, but it has
> spawned numerous spurious copycat stories that are standard April Fool's Day
> fare. Heinlein's is just the most immediately credible. The state in
> question is always some state presumed inhabited by rustics. But no state
> in the U.S. has ever had a law passed legislating the value of pi. Indiana
> came close.
>
I annoyed my HS geometry teacher by announcing I could trisect an angle.
True, a Carpenter's Square is illegal under the rules of "Geometric
Construction", but I could easily prove that it worked.
There are other methods, using other tools, but a carpenter's square is
probably the easiest to prove correct.
On Mon, 23 Aug 2004 16:47:43 -0400, Ken McIsaac <[email protected]>
wrote:
> I
>actually computed a fifth order polynomial approximation to the chair
>leg curve I wanted on a table I made for my mother-in-law last year.
That one I'd like to see.
>Unfortunately, I have learned that I can do the math, but I can not
>cut these crazy dimensions accurately. From now on, it's 90 degrees
>or 45 degrees or re-design it because it's wrong.
Then your own designs are fairly simple. I admire people who do their
own design. It's not the math, it's art. The math I can do easily,
and often apply it in the shop, or on the computer or wherever, but
the art? Stick people are beyond me. I need plans with numbers on
them mostly. I did figure out how IKEA designed their neat folding
table though.
Bill.
On Tue, 17 Aug 2004 13:49:35 GMT, "Bob Schmall" <[email protected]>
calmly ranted:
>
>"David F. Eisan" <[email protected]> wrote in message
>news:[email protected]...
>> See a Rabbi.
>>
>> Oh, that's something else, nevermind...
>
> How long is a mohel?
Is that what you're making this mountain out of, Bob?
--============================================--
Growing old is mandatory; growing up is optional.
---
http://diversify.com Comprehensive Website Development
On Tue, 17 Aug 2004 01:14:50 +0000, moyo wrote:
> knowing that the diameter of a circle is 32 and 1/2 inches, How do I
> figure the outside length of the disk.
Pi times the diameter. Two times pi times the radius. Pi is 3.141592654
(Pi has infinite digits beyond the decimal, but your calculator doesn't
care.)
102.1 inches.
--
"Keep your ass behind you"
On Tue, 17 Aug 2004 05:56:37 -0400, "Mark Hopkins"
<[email protected]> vaguely proposed a theory
......and in reply I say!:
remove ns from my header address to reply via email
>My, My....thats an awfully big pi...
wi?
102.101761241668280250035909956584
>> "Keep your ass behind you"
Iiiii Knoooowwwww! My donkey kicked me in the behind just the other
day....
*****************************************************
Marriage. Where two people decide to get together so
that neither of them can do what they want to because
of the other one.
On Wed, 18 Aug 2004 08:37:08 -0400, loutent <[email protected]> vaguely
proposed a theory
......and in reply I say!:
remove ns from my header address to reply via email
100 seconds to the hour, ten hours per day, 100 days per year.
All this would be possible, if only we could round off Pi.
>Now if you live in Indiana, you can simplify
>your Pi calculations.
>
>If you've never heard this story, it's an interesting read:
>
>http://www.agecon.purdue.edu/crd/Localgov/Second%20Level%20pages/Indiana
>_Pi_Story.htm
>
>Lou
*****************************************************
Marriage. Where two people decide to get together so
that neither of them can do what they want to because
of the other one.
On Tue, 17 Aug 2004 11:11:27 GMT, "David F. Eisan"
<[email protected]> calmly ranted:
>See a Rabbi.
>
>Oh, that's something else, nevermind...
I believe you were referring to theese, Meester Ironmonger:
--Three Samurai--
Once upon a time a powerful Emperor advertised for a new Chief
Samurai.
Only three applied for the job: a Japanese, a Chinese and a Jewish
Samurai.
"Demonstrate your skills!" commanded the Emperor. The Japanese
samurai stepped forward, opened a tiny box, and released a fly.
He drew his samurai sword and "swish"; the fly fell to the floor,
neatly divided in two!
"What a feat!" said the Emperor. "Number Two Samurai, show me what
you cando." The Chinese samurai smiled confidently, stepped forward
and opened a tiny box, releasing a fly. He drew his samurai sword and
"swish, swish"; the fly fell to the floor, neatly quartered!
"That is skill!" nodded the Emperor. "How are you going to top that,
Number Three Samurai?" Number Three Samurai stepped forward, opened a
tiny box, released one fly, drew his Samurai sword, and "swoooooosh"
flourished his sword so mightily that a gust of wind blew through the
room. But the fly was still buzzing around!
In disappointment, the Emperor said, "What kind of skill is that? The
fly isn't even dead."
"Dead, schmed," replied the Jewish Samurai. "Dead is easy.
Circumcision--THAT takes skill!"
--/Three Samurai--
--============================================--
Growing old is mandatory; growing up is optional.
---
http://diversify.com Comprehensive Website Development
My, My....thats an awfully big pi...
"Australopithecus scobis" <[email protected]> wrote in message
news:[email protected]...
> On Tue, 17 Aug 2004 01:14:50 +0000, moyo wrote:
>
> > knowing that the diameter of a circle is 32 and 1/2 inches, How do I
> > figure the outside length of the disk.
>
> Pi times the diameter. Two times pi times the radius. Pi is 3.141592654
> (Pi has infinite digits beyond the decimal, but your calculator doesn't
> care.)
>
> 102.1 inches.
>
> --
> "Keep your ass behind you"
>