# Optical Forums > Ophthalmic Optics >  Resultant prism

## John R

Does anyone know the forumla for working out resultant prisms ?
You know the kind where someone orders 9 down & in @ 295.
We need to know how much in each direction.
Well our chart only goes to 6 diopter's of prism and our lab program needs the ammounts of prism in each direction not the combined ammount.
Yes i know i could half the ammount and get the answer (which is what i did) but i thought it was time to strain the brain and do a new one  :D

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Every day a grind
Every week a bind
www.iooi.co.uk

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## Judy Canty

V=(P)(sin a)
H=(P)(cos a)
where P=the amount of the resultant prism
      V=the vertical component
      H=the horizontal component

I'm no expert, it's in my Optical Formulas Tutorial by Ellen Stoner and Patricia Perkins.
Hope this is what you're looking for!

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## Pete Hanlin

A non-formula method of converting the prism is to use graph paper.  

For example, if the boxes of the graph are 1cm per side, pick a point in the middle of the paper and use a protractor to draw a line 9 centimeters long from the point at an angle 65 (360-295) degrees down and to the right.

From the starting point, measure the number of blocks across (in) and down to get the components of the prism.

Pete

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## Pete Hanlin

BTW, I don't have a protractor handy... but if I guess at the 65 degree angle, I'd say the resultant prism should be around 7.25 down and 5.50 in.

Pete

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## Darris Chambless

Hello John,

With a little artistic help from Maria it should come out to be 4 base in, 8 base down.

The only formula I have is for determining resultant prism. I can't find the one for the reverse.

Take care,

Darris C.

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## Maria

'A little artistic help', meaning I did all the working out, and I'm the only person involved with a protactor.  :)

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## Maria

Ok, I THINK the equation is this, but don't believe it until it is confirmed by someone else.  :)

This is all half-remembered school stuff, BTW.

You need to convert it into 180 degree format first of all, and that gives you the three angles of your triangle, because one will be 90, and the other will be 90 - the one you have.
Then the equation is hyp sin angle, where hyp is the distance given in the single resultant prism. The answer is always the side of the triangle opposite to the angle.

And you really should have asked this when I was 15, and actually knew what I was talking about.  :)

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## John R

Thanks folks for the answers  :D
Will have a try at the formula to see if it works.
Maria I never knew you were the artty type  

------------------
Every day a grind
Every week a bind
www.iooi.co.uk

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## Pete Hanlin

Now that I have a protractor handy, I see that the angle I estimated at 65 degrees was more like 54 degrees.  If you use the correct angle, Darris' (er, Maria's) answer is correct.

Pete

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## Blake

Actually, Pete, 65 degrees was better, since 360-295=65.  You'd get the same numbers, but up instead of down.  

Using the formulae that Judy posted:

9*cosine(295)=3.80356
9*sine(295)=-8.15677

So it's roughly 4 in and 8 down.  It helps to have a good calculator handy, or tables of sine & cosine values if you like to torture yourself.

To find the resultant prism, square both components, add them, and take the square root.  Using 4 in and 8 down:

sqrt(4^2+8^2)=9 {approximately}

To find the angle, you have to find the arctangent of the vertical divided by the horizontal...

arctan(-8/4)=297 degrees {approx.}

I know, it's not as much fun as watching grass grow, but it allowed me to waste a few minutes ;-)

Blake

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## Joann Raytar

Blake:

Would that be the old Phythagorian Theorem you would be referring to?

a squared  +  b squared  =  c squared

[This message has been edited by Jo (edited 04-27-2001).]

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## shanbaum

> Originally posted by Jo:
> _Blake:
> 
> Would that be the old Phythagorian Theorem you would be referring to?
> 
> a squared  +  b squared  =  c squared
> 
> _


It is exactly that.

But it's spelled _Pythagorean_.


[This message has been edited by shanbaum (edited 04-28-2001).]

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## Maria

Mine has Pythagoras in there somewhere, but a lot of the Garble theory pushed it out. 

Maria 

BTW, I checked my spelling of Pythagoras, because I was afraid.  :)

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## Kevin Howtopat

Seems to me like it would be a lot easier if You just put nine diopters of prism at 295 and left it at that

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## Blake

Kevin,

John said his lab program required the vertical and horizontal instead of the resultant.  You can't argue with a computer... they always get their way in the end.

Blake

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## John R

Yes it would but our laying off prog wont accept that form it needs to know both ammounts of prism, and work it out its self. Stupid i know but its a home grown program that suits our needs  :D True we could alter it by hand, keep telling them that myself but some folks just wont listen   also altering by hand need someone who knows what they are doing or the prism could end up the wrong way, as its amazing how many order it wrong eg 9.0 @ 65 then state down & in.

------------------
Every day a grind
Every week a bind
www.iooi.co.uk

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## Darris Chambless

Eh Hum,

Maria left out a little information so I thought it might be appropriate to fill in the blanks...:-) As I stated Maria did the art work for me because I couldn't find my protractor. So I asked her via MSN Messenger service, if she had one handy.
Originally she said that she did, but I later found out that she was working it in her head (which means the accuracy could very well be questionable ;-) so I had to explain that I needed her to physically draw the picture. THEN she actually went and got her protractor and we started all over again.

Well, I talked Maria through the ENTIRE picture STEP by STEP and had her measure where I TOLD her to which she did. She then relayed the measurements to me and I said "Thank you." I then gave the artistic aspect credit to Maria and gave John the answer. Basically I was the supervisor with all the knowledge and Maria was  my "lackey" :-)

So credit was given where credit was due in my original post. And yes, obviously Maria can draw a straight line when and where she's "told" to. :-)

Thanks for listening,

Darris "I did all the thinking and she just drew lines :-)" C.

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## Maria

A rather creative version of "I typed out Pete's instructions. I then realised Maria was only pretending to work it out, and had not bothered to fetch protractor, pen or paper. I whinged and whinged and whinged until she did it properly. At no point did I inform her that I was using Pete's instructions, or indeed that it was for the board, preferring instead to give the impression that it was for my work. Maria is better than me."

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## Darris Chambless

Maria, Maria, Maria,

If you could check the time coding you would find that I was talking you through this mathematical problem at the same time Pete was probably writing his response. Therefore Pete's instructions weren't available at that time. Also if it's still there from the old board I worked a similar problem about three years ago regarding resultant prism the same way.

So there. Nyeah! :-)

Pete (being as brilliant as I am and as the old saying goes "Great minds think alike." ;-) was simply working the problem out the same as I did but without your protractor :-)

Well I must be off to grace others with my unending knowledge and intellect :-)

Love always

Darris "While you were away I solved the worlds problems" C.

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## John R

Darris You do know we have foot and mouth over here  Well as Maria is coming your way soon you could end up with your own case of it............

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## Darryl Meister

Didn't anyone read my posting in which I declared the Ophthalmic Optics forum a tranquil "optical oasis"?!?

And must our two nations still bicker like this, long after our country already proved its obvious superiority over the British?!?  ;p

(That's just a joke... British folk, please do not take offense. I could never belittle the country who gave us Monty Python.)

Best regards,
Darryl

[This message has been edited by Darryl Meister (edited 04-30-2001).]

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## Shwing

Holy crap!!

I just spilt my beer!!

It's ALIVE!!!!!

Howdy, Mr. M....

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## Pete Hanlin

Let's see... how _would_ Monty Python have answered this question?

"And having taken the Holy Protractor and having protracted to 65 -and neither 64 nor 66- thou shalt take the Holy Pencil and make a ray..."

"What's all the commotion?  Its only a bloody prism!"

"But its in degrees!"

"Run away, run away!!!"

Pete "bring me a shrubbery" Hanlin
PS- Could it be the oasis was a mirage?

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## John R

Just one word for that "Pete" me thinks
* SPAM*

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## Maria

Just remember people, Darris isn't the Messiah, he's a very naughty boy.

(This is from the film "Life Of Brian", and not some sort of prostitute talk, see next page for details :))

[This message has been edited by Maria (edited 05-01-2001).]

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## Darris Chambless

Yes Maria,

But that's because you haven't been the dominatrix that your suppose to be. That's the only way to keep me from being "naughty" :-)

Darris "naughty" C.

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## Maria

I feel sick. Does anyone else feel sick?  :) It's like when you see documentaries on TV about hookers, and there's those middle-aged men who dress up as babies.

If this is an oasis, I think we've just found the sewage outlet pipe that the brochure didn't mention.  :)

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## Joann Raytar

This is the last time I go straight to page 2 of a thread without reading page 1 first.

Scary, very scary ...

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## Darryl Meister

Obviously, Robert and I need to put tighter stipulations on the kind of riffraff we allow into the Ophthalmic Optics forum.

Apologetically,
Darryl, Your Forum Moderator

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## John R

I dont see any post's from riffraff are they a new member  :D

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## shanbaum

Sorry - what's going on?  I was tied up...

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## John R

> Originally posted by shanbaum:
> _I was tied up..._


Well well, were you now    
Hope the ropes were fur lined   

Well it started about wanting to know the formula for resultant prism and some how got to this stage.... I blame the Mods.....


[This message has been edited by john r (edited 05-02-2001).]

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## Darris Chambless

Hello to all,

I'd just like to say for the record that Maria started it :-)

Darris "A victim of circumstance" C.

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## Maria

Isn't Riffraff the one who goes to Transylvania with his sister, to forge a new career presenting the Crystal Maze?

[This message has been edited by Maria (edited 05-02-2001).]

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## John R

Oh you rocky horror babe

thread takes an even stranger turn  :D
we had sado mac....
now tranvestisiam  
and all this from a convent school girl  
Now wheres my ...........

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## Pete Hanlin

So I suppose we've gone from _Monty Python_ to the _Rocky Horror Picture Show_ (did that movie ever make it to Europe).

Steve is going to have to put a rating system on these strings...  this used to be a "family web page" (yeah, right!).  I wonder how often OptiBoard is going to pop up on search engine pages now that the dark worlds of bdsm and transvestitism have invaded our "little Oasis?" 

As for me, just the thought of Darris and Maria being in my house at one time (having met Darris already  ;) ) is beginning to worry me   !  

Pete

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## Darris Chambless

Pete,

Deal with it. :-)

Darris C.

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## Pete Hanlin

I have commenced dealing...  :)

We need to nail down the dates Maria is coming (haven't heard from her lately) to try to coordinate your visit- should be a blast!

Pete

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## Darris Chambless

Hello Pete,

It will be a blast. We could get arrested this time I'll bet :-)

Darris C.

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## John R

> Originally posted by Pete Hanlin:
> _Steve is going to have to put a rating system on these strings...  Pete_


You dropping hints bout the new board there..  :D
I will look forward to the news for any bits about 2 yanks and a lone brit in florida. Could end up like butch and sundance eh.....

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## Maria

> Originally posted by Pete Hanlin:
> _ (did that movie ever make it to Europe)
> _


Before it was a film, it was a West End musical, so there  
I am coming on the 13th Aug, and leaving on the 27th. I have also placed it on the calendar of a website that isn't this one.

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## hcjilson

Holy Mackerel!!!! If I'd have guessed what was going on here....I would have shown up earlier!Last time I was here I got blown out of the water so I decided  to leave well enough alone. Dominatrix INDEED!!....MOMMY??Yes  you will be able to check the calendar out starting Monday we hope! To whomever suggested starting at page 2 of this thread....Thank you...you have given me new faith!

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## hcjilson

John, why not come over at the same time-you have a roof over your head on Cape Cod anytime you want.I guarentee you will be cooler than at Pete's in August-
Best HJ

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## Joann Raytar

Be careful John; remember the Boston Tea Party?  You just might find all of your belongings floating away in the Hyannis Tea Party.

[This message has been edited by Jo (edited 05-03-2001).]

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## Darryl Meister

> Originally posted by Maria:
> _Isn't Riffraff the one who goes to Transylvania with his sister, to forge a new career presenting the Crystal Maze?_


Well, when the sequel to the Rocky Horror Picture Show flopped (the one about the asylum), what choice did he have?


[This message has been edited by Darryl Meister (edited 05-03-2001).]

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## John R

> Originally posted by Jo:
> _Be careful John; remember the Boston Tea Party?  You just might find all of your belongings floating away in the Hyannis Tea Party.
> 
> [This message has been edited by Jo (edited 05-03-2001).]_


Why they called it a tea party is beyond me as the 2 words dont realy go together well, unless it was thw wi holding it, now if it was beer party  :D I alway travel light so there wont be much to float away. (wife takes kitchen sink so no room for my stuff  )

HC thanks for the offer one day maybee....

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## Joann Raytar

Another handy website:

*Optical Formulas Instructor*

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## Cj Eggbeer

Dear Pete,

I'm happy to know that I'm not the only one that has had to resort to using graph paper to understand prisma.  Did you invent the technique or do you know who did?

I'm new to the board, so I won't bore you with my prism formulas until I get that $%^&#@ novice tag off my name.

Sincerely,
Cj

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## Cj Eggbeer

To all...

Sorry to spoil the mood of this thread.  In the future I'll check out page 2 before I post.

As you were...

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## John R

> _Originally posted by Cj Eggbeer_ 
> *Dear Pete,
> 
> 
> I'm new to the board, so I won't bore you with my prism formulas until I get that $%^&#@ novice tag off my name.
> 
> Sincerely,
> Cj*


Please DO   bore us with them it will be a change from Pete or Darris doing it.. :drop: and get you off the Novice tag....

Jo once again you hit paydirt :D
and it's even got a link to this site :bbg:

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## mullo

Jo, I must say that I have saved several of the links you have provided in my favorites, just below Optiboard of course. So Thank You, Mullo

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## Joann Raytar

mullo:

:D Your Welcome!  You should see my Netscape Bookmark files; I always was a pack rat.

- Jo

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## Darryl Meister

> _Originally posted by Cj Eggbeer_ 
> *I'm happy to know that I'm not the only one that has had to resort to using graph paper to understand prisma.  Did you invent the technique or do you know who did?*


Just remember that all we are really doing is just the general process of converting between rectangular (e.g., base in, base up, etc.) and polar coordinates (e.g., base @ 45) -- applied to prism, of course... A technique that has actually been around for a couple of centuries by now. Part of all that boring stuff they taught us back in high school. ;) Most cheap scientific calculators even have a little button you can use to convert between the two automatically.

Best regards,
Darryl

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## Pete Hanlin

> _Originally posted by Darryl Meister_ 
> *
> 
> Just remember that all we are really doing is just the general process of converting between rectangular (e.g., base in, base up, etc.) and polar coordinates (e.g., base @ 45) -- applied to prism, of course...*


Well, when you put it like _that_!  

Next time someone asks if there's an easy way to figure out what prism(s) would result from a prism given in degrees, I'll say "Sure, you just convert from the given polar coordinates to the rectangular coordinates using a protractor, a surface with a non-arching edge, and graph paper with equidistant reference demarkations...  With a few simple measurements, the resulting prism will become palpable!"

Let's see, I think Steve should build a web site to convert common language into "Darryl-speak!"  Hmmm, it might work something like this...

_"Please turn on the lights."_
*Translation:* "By closing the circut to the source of alternating electrical current, please illuminate the confines of this rectangularly shaped area via the horizontally oriented flourescent devices which have been mounted to the upper defining surface of the aforementioned area."

Just kidding...  I've watched Darryl solve dozens and dozens of optical problems during the past few years in his role as our resident Opti-scholar.  If _Who Wants to Be a Millionaire_ ever has an optical version of the show, Darryl will undoubtably breeze through with his lifelines intact.  Plus, its nice to settle any optical related dispute by simply stating, "but Darryl said..."   ;)

Pete "I stand in awe in the presence of the superlative of optical greatness" Hanlin

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## Steve Machol

As a special treat for our British cousins, I've translated  Darryl's statement into Cockney.  Hopefully this will foster an increased understanding between our divergent cultures.  :bbg: 




> Just remember that all we are right doin' is just the general Queen Bess of convertin' between rectangular (e.g., base in, right, base up, etc.) and polar coordinates (e.g., base @ 45) -- applied ter prism, o'course... A technique that 'as actually been 'round for a couple of centuries by now. I'll get out me spoons. Part of all that borin' stuff they taught us hammer and tack in 'igh school. Most cheap scientific calculators even 'ave a wee button yer can use ter convert between the two automatically.

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## John R

> _Originally posted by Steve Machol_ 
> *As a special treat for our British cousins, I've translated  Darryl's statement into Cockney.  Hopefully this will foster an increased understanding between our divergent cultures.  :bbg: 
> 
> *


By eck lad you may as well have translated it into outer Mogulian Steve :hammer: as us northerners cant understand cockney any more than you can understand canidian :cheers:
I think that we (Maria & me) are begining to get the jist of what you are yanking on about most of the time though  :Confused:

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## Darryl Meister

> _Originally posted by Pete Hanlin_ 
> *
> Let's see, I think Steve should build a web site to convert common language into "Darryl-speak!"  Hmmm, it might work something like this...
> 
> "Please turn on the lights."
> Translation: "By closing the circut to the source of alternating electrical current, please illuminate the confines of this rectangularly shaped area via the horizontally oriented flourescent devices which have been mounted to the upper defining surface of the aforementioned area."*


Well, unless it was in an automobile, in which case it would be "direct electrical current" and an "incandescent light source" -- or perhaps even a "vacuum-enclosed tungsten filament heated to 3,600 Kelvins." ;)

Best regards,
Darryl "Let's not propagate any more optical myths and misnomers than we absolutely have to" Meister

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## Cj Eggbeer

Hi Darryl,

So you're saying it might have been Euclid, around 300 B.C., or even Pythagoras himself, c. 600 B.C., that first used graph paper to explain how to neutralize or verify Cartesian prism with the reticle of a lensometer? :-)

Best Regards,
Cj

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## Darryl Meister

Hi Cj,

Are you implying that calculating prism with graph paper is somehow different than calculating the distance to some point (x,y) like you did back in 8th grade mathematics? ;) Like I said, it's the exact same process, but applied to prisms. Trust me, the graph paper doesn't care whether your lines and arrows represent prisms or velocity displacement vectors. And I would certainly say that the Rene Descartes (1596-1650) most likely did a great deal of work with his Cartesian coordiante system over 300 years ago. And, while he and his successors didn't have the benefit of a Wal-Mart to purchase "graph paper" from, I'm sure that they made do with regular parchment, a rule of some sort, and a pen. ;)

As far as strictly prismatic applications go, the oldest book on dispensing I have (1951, from Russell Stimson) describes how to use graph paper for prisms. (Inexpensive calculators weren't available back then.) By the way, just to be clear... The point of my earlier response was not to detract from the value of your suggestion, but rather to explain the process is a general one, which has been around for some time. Although calculating it will be more accurate than drawing and measuring it, performing the excercise of using graph certainly gives you a better intuition and understanding about prism in general. A rough sketch, even without the aid of graph paper, is also good to verify the calculations and to make sure that you have the signs and directions correct.

Best regards,
Darryl

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## Cj Eggbeer

Dear Darryl,

Not implying anything here, just trying to have a little fun while I learn.

Actually, Pete's comment about the graph paper caught my eye because it reminded me of a time, about twenty years ago, when I was an underpayed, overworked, barely qualified lab manager who had to figure out a way to verify that my lab was producing compound prism correctly.  I didn't have a mentor, and couldn't afford the books or the surface calculation program (RXP I).  We had calculators back then, but the ones that converted degrees to radians and back were about $100, or three weeks worth of groceries.  TCP/IP was still more or less on the drawing board, and the OptiBoard wasn't even a glimmer in someone's eye yet.  We didn't even have Wal-Mart back then, unless you lived in Arkansas.  I didn't have the time to run through the calculations manually, what with the customer waiting and all.  What I did have was graph paper, my trusty pd stick, and a protractor.  Voile, problem solved.  Thanks for the memories, Pete.

About the eighth grade, after riding Betsy the cow 20 miles through knee deep snow to get to my one room school house, I was frankly to exhausted to remember geometry or algebra.

Sincerely,
Cj

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## Pete Hanlin

I'm just glad someone else appreciates the "elegance" (in arithmetic, when you solve a problem without extra steps, the solution is said to be "elegant" - at least I think that's the term), of using graph paper and protractor instead of prolonged computations...

BTW, Darryl mentioned that automobiles have direct current.  Did you know the car makers are seriously considering bumping the typical car's voltage from 12V to 36V- just to handle the drains placed on the electrical system by our modern stereos, ECMs, A/C, dozens of little running lights, defrosters, and so on?  Seems when they adopted 12V they didn't imagine the accessories cars would one day have (kinda like the fella who decided we would only need 640k of base memory way back when ;) ).

Here's to Darryl's health!  :cheers:   May he always be around to solve our more perplexing problems!

Pete

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