Tangent Circles: Newsletter Challenge (07/24/07)

All that the unspecified n and r actually tell us is that the circles must all be of the same radius. Read with the statement "several circles that are all tangent", can be taken as a number of identical circles, all tangent to each other.

This would give either two circles, or three circles, the latter so arranged that their centers are on a equilateral triangle of side 2r.

But this sounds to simple for a CR4 challenge, so where is the catch?

Jorrie

Not certain he means circles that are all tangent to every other circle, but it doesn't impact the technique. They could all be tangential to a single circle, or we may be over-interpreting. However, apart from the possibility that you don't wish to reset the compasses, or that the maximum radius they can attain is R, I can't think of anything.

Doubtless the finest minds of CR4 will find something we have missed.

It may be required that the drawing be created with only the compasses and a reference length as tools (no straight edge or protractor). I think I'd be inclined to build the matrix using the vertices of equilateral triangles of side R, rather than 2R, but it depends on size and the quality of the compasses.

Fyz

For n = 2 the solution is trivial.

For n = 3 the solution as above is a triangle of sides l = 2r and each circle touches every other circle.

For n > 3 the solution is essentially the same as for n = 3 except that each circle does NOT touch every other circle.

Seems to be too simple to be a challenge. What have I missed.

Or is it possible that we can create an array of uniform triangles and omit a few of the circles to achieve a unique design?

I haven't read all the posts, but the problem never said the design had to be two dimensional.

Inscribe four circles on the faces of a regular tetrahedron and all are tangent to each other.

If anyone has drafting software for N dimensions where N > 3, then I bet we could create a similar solution in those higher dimensioned spaces, too.

One solution I didn't see addressed, perhaps cheating, is for an infinite # of circles to be superimposed on each other.....

You were all right gentlemen.

I don't see any catch. The post I believe solicits for the fastest way to do the task in CAD, which I believe you have concluded very well.

Draw first an n-polygon of sides 2r and then drawing n circles of radius r having centers at the polygon's vertices.

Of course n will be limited to 2 or 3 if the case is that all circles are tangent to each and every other circle. For n equals 2, then n-polygon becomes a line having length of 2r.

Cheers...

As above, it doesn't specify that "all are tangent to all adjacent circles", which would just be a grid, or that "all are tangent to all the others", which would be interesting past n=3, maybe an overlapping donut like array without a hole? (3D => n=infinity) All it says is that it is "based on several circles that are all tangent"... Draw whatever you want, the person was not specific enough.

Personally, I'd just 3D sweep a donut shape in small increments, but I'd leave about 30 degrees so it looked like pac-man, then make a comic caption of it saying, "Tangent to what exactly?"

If it means all circles at 90 deg to each other and touching, and the points of contact are concidered to be tangent to every other circle? then you can use an array, n number of rows n number of columes spaced 2r apart. Just a stab in the dark.

You are right, I was making the drawing as small as possible for the number of circles, but the question does not specify this. We could place them along a straight line if we wished...

A. The only way that all circles of the same radius can all be tangent (outside) to each other is when the number n=3. their centers form an equilateral (sometimes described as "equiangular") triangle with sides of 2r. When n=2,4,6,8,..., only two circles of equal radius can be tangent same time regardless of arrangement.

B. When the n number of circles are of different radius r only 2, 3 and max of 4 can be all (outside) tangent at same time.

C. If you consider inside tangential where circles are of different radius r, then all the circles from the larger to the smaller can be all tangent at a common point same time.

Why only two dimensions? Each circle has only two but the construct needn't.

In 3-dimension, consider a torus of a circle radius r same radius as the torus, meaning n number of equal radius circle tangent at a common point at the center of the torus.

Looks good to me - same as #5 but the explanation helps.

Fyz

Like this:-

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The other design with more than 3 circles Which others have hinted at would be the four incircles on the faces of a tetrahedron.

Slinky!

Is the CAD bit of any interest?

Fyz

Hi Randall, crafty!

This explains the r and n, here meaning an unlimited number of circles, all of same radius and all tangent.

Jorrie

I can't really take the credit for that; I was just drawing what other people had described.

This:----------------

which was more or less my suggestion was surprisingly much more difficult to draw.

R is a single value, n is a single value not variable, as math notation here says,

drawn on a computer pick a number for r that fits the other half of the equasion, then solve for remaining term and umm by then you will have drawn it on the computer too, thus fulfilling the question..

As guest (probably an alias) said in post #5, you could have n approach infinity, the space between the individual circles approach 0, and end up with an array that looks like a donut without a hole.

Yes, exactly, at some point in the billion range, n could produce a ... ball and at close to infinity, a black hole of ink.. or elctrons..

if r increases then this ball would exceed the size of the universe and allow n to be even closer to infinity, and thus the present universe could be completely swallowed up in such huge dimensions.

well who really knows what happens when things go infinite?

but this prob limits it to what you can draw with the computer drafting prog. so there is a maximum value for both r and n

jstacat

Odd-shaped ball. How would you create such an infinite structure on a CAD system? Do you know the universe is spatially finite? (Anyway, if the centre of the toroid was in our universe, there would always be the infinitesimal double-sided funnel that wasn't included)

This design reminds me of a very orderly illustration of the Van Allen Belt that "encircles" the earth. Cheers Mint Condition

randall....perfect replica, as for cad reference, i would normally use a circle (r) and a tangent axis and then revolve or 3d array the circle around the axis...problem here is the infinite n of circles.....the drawing becomes a solid torus shape

Each circle subtends an angle of 360/n.

The circles to be drawn are at a distance of r/ sin(180/n) from the central point.

So with 10 circles to be drawn of diameter 15 whatever's, you first draw a circle of radius 15/sin(18) = 48.54. You then chop the perimeter into 10 bits and draw circles of r radius.

Well I dunno, it's got to be something like that. I never use CAD. I've probably made a good howling mistake, but that's why a bit of pen and paper is better.

Oh what the hey. This looks interesting. Farey series comes into this somewhere as well ( something to do with 1 circle contacting 2 adjacent ones).

As an old pool player who has played seven-ball a few times, I'd say n = 7, regardless of the radius.

.

Lets just say that it is a globe made up of infinite circles.... a ball..

I say zeke, didn't get his name for nothing. He's absolutely right.

I have to agree with the rhombus theory seems like its the only way all circles can be tangent to one another. So the easiest way to draw in in cad would be to select the rhombus in 3d and set the center point at zero... yes, no, maybe?

I have cad I use cad But I still suck at the 3d stuff..... lol

My apologies to everyone for the confusion. I am the author of this Challenge Question. I'm not sure why GlobalSpec didn't metion that.

I was sparing with my words in order to come under the 75 word limit, and so I left out vital piece of information. I was going to post that info, but a power spike knocked out my cable modem. Good thing it was under warranty.

Anyway, what I should have said was "every circle is tangent to the 2 adjacent circles." In even fewer words, it's a ring of tangent circles. What I am looking for is a method to do this with a CAD program, but someone could do this manually as well.

Someone has already given the answer, but I won't say who.

I have another CQ ready to submit, and it should be intriguing if they use it.

A ring of N touching circles in a perfect circle? Two simple ways to do this, I think

1) Draw lines of length R*cosec(180^O/N) all projecting from a common centre point, with angular separation of 360^O/N. Draw the circles with their centres at the outsides of the lines. Then delete the lines. I think this is equivalent to Kris' method (ignoring mistypes).

2) Draw a regular N-sides polygon whose sides are 2R. The angle in each vertex needs to be 180-360/N degrees. Then place the centres of the circles on the vertices. Then delete the polygon.

In most CAD systems, the lines for either version can readily be placed using copy and rotate (about a defined point). Kris' method is probably simplest, as you can rotate about the same point each time.

Fyz

As far as I can tell, we are agreeing Fyz. This is worrying so I shall attempt to stop it. Some might suggest I should have written 'Sine' instead if 'Sin'. Likewise 'Cosecant' might be offered instead if Cosec. Ignoring the capitalization issue, my own view is that using a whole new word to describe an inverse function is unnecessary (though it does have the advantage of allowing me greater scope for misspelling). Finding much pleasure in sharpening pencils, I have never been that attracted to CAD but one possibility may interest me: Can you press a 'polygon [n]' type of key to generate the polygons 'spokes' + draw the circles [r] and allow the software to just float the circles down between spokes to a point of contact (between adjacent spokes). Being able to drag-and-drop circles in the approximate position then watch them slowly bounce and settle (whilst moving toward the common centre of the shape) might be nicely relaxing. To clarify my meaning, it would be like watching a scoop of ice-cream falling from height into a cone (this 3D analogy is more complex because it would produce a football shape in one extreme, but it sounds more fun than a 2D analogy). The software would presumably churn out the calculations that I had already done by hand, but I might get paid lots for having hours of fun.

Other than your mistypes, I think we agree completely. I was taught that sine and cosine may be written out in full in text, but the short forms are universally used in equations, and without any abbreviation marks. Secant and cosecant are good if you want to write equations without quotients, and I generally avoid quotients from habit (where possible); this is because printers so often insist on using a horizontal line for the quotient, which messes up the column-inch allocation. It wasn't relevant in this case, so apologies.

Your question - some CAD systems will generate regualar polygons direct, with or without spokes; but unless you use them a lot, in many cases it's more trouble than it's worth to find the tool. Could this be why "being bolshy" seems to have become part of the CAD professionals' job description? (If you are a CAD professional, responding in kind will be deemed as demonstrating the case - damned of you do, darned if you don't)

Other than your mistypes, I think we agree completely.

!

Maybes there no all mistypes.. I need grammer-o-matic too. So if we agree (OK , we do) and we is right and 3-Doug is giving prizes who gets it ? Being already damned I'm quite happy Ether way. Some very naff/old CADware lurks on my machine, I've simply never bothered looking at it. Perhaps I will take a peek sometime, as it may be useful for something sometime. It's a bit like the fondu-set/chop-sticks/chicken-brick/....all culinary items I have. Hang on, 90 % of all my possessions (avatars excepted) of any sort that languish in dark corners of my cave. Until somebody starts a new thread on tides, I am *.

* Disclaimer - that topic only, and subject to my daily whim.

You get the prizes. I'll take my reward when (finally) I get to hell.

A certain red-caped figure tells me we can share the prizes and rewards one day, whilst discussing the aerodynamic merits of chicken-bricks etc. I'm sure ER can provide a suitably medieval style rotisserie.<grin>

oh yes....complete with self-rotating mechanism.

...Somehow I just knew ! The wonders of CR4 . LMAO

Curious: I use quotients to avoid having to to remember any trig functions beyond sin, cos, and tan! And I've been quite successful at not remembering the others...

I'm hardly a CAD professional, but I sure can't imagine doing any but the simplest sketches with pencil. There's no way hand drawn images will show me the clearances between various parts of a machine, and quickly allow me to rotate or slide parts to various positions to see what interferes with what. My big limitation is that I've only learned the most rudimentary functions of 3D - hopefully that will change soon...

The first time I read your post #14, I just skimmed over it, since the challenge said to use CAD, but you clearly had the concept correct.

Dick

Hi Dick, One of the posts you refd. to was Fyz and the other mine. No matter, I'm confused anyway. Just wanted to ask , does anybody else here have " Some Of Harry's Cows And Horses Trod On Arthur" etched in their brain from School ? I'm sure there must be other ways of remembering. Methods in non-English languages would probably translate really strange. By the same reasoning, my memory aid would sound weird in French/German etc ('except being Brit I never learnt any other languages.). I have to admit that CAD is pretty cool, but I wonder if young people today get any grounding in 'normal' tech-drawing. Even if I was capable with CAD I'd still do rough pencil calculations. Teachers could probably tell of some achingly bad mistakes where students have not done a quick check (to make sure an end result/units etc looks approximately right).

Took me a while to work outs what you were on about Kris. We just used SOHCAHTOA - it always reminds me of Krakatoa...

What about ACTS to remember which ones are positive in which quadrant.

I never could see the point in those diversions. In fact, I would almost be inclined to ban them as encouraging too much memory use. They require that you associate an unconnected word, and remember a meaning for each letter... For semi-dyslexics like myself, they also move the thought process into additional words, when what you are working with is essentially visual. (It's a bit like teaching arithmetic by rote before you get the children counting on their fingers...)

If you start with Tangent, the name implies the tangent to a circle. The first letter T draws a tangent and a radius, with the tangent above the radius. The only place for the angle is at the centre of the circle => opposite over hypotenuse. I agree it's more convoluted, but there's less to remember, and it involves the correct part of the brain.

Given that as a clue, it's best to let the students work out their own method for sine and cosine. My maths teachers did this, and it didn't do me any harm... (you decide)

Regarding the quadrants, you can either use a mental geometric drawing or continuity in the graph. I used to do the former, but when I was involved with electrical engineering I saw so many d....d graphs... (all together now - aaah)

Fyz

aaaaaaaaaaaaaaaaaaaahhhhhhhhhhhhhhhhhhhhhh ! (I'm sure it should have a r in it)

Maybe the question could have just said 'touching' instead of 'tangent'. It sounds more appropriate somehow. Sort of moving. <gentle sigh,bless.>

I found SOHCAHTOA useful - and when I had to do some geometry recently, that was what I remembered and found useful. However, we were also supposed to learn by heart some (9) equations that related the sin(θ) = cos(θ±π/2) equivalent angles theory in all quadrants - or something. I wrote it all down whilst reading a book and at the end of the lessons, said I didn't understand (I picked up "learn these by rote to pass your exam" and though s*d that!) so my teacher drew a little sketch showing cos and sin functions over 360° and said that the equations were so that you could work out the identities for equation substitution.

My exam papers from that year on were peppered by little sinusoidal sketches with vertical and horizontal lines on to work out the equivalent angles...and I never did bother to learn those pesky equations...first principles were easier to remember and to process!

the ACTS one is visual:

...A..|...S
‾‾‾‾‾‾‾‾‾
...C..|..T

[apologies, I'm *rap at text "graphics"!]

So in the first quadrant all are positive, second only sin, third only tan and fourth only cos. Mind you, to double check this I just drew three little sketches...so I refer you to my previous statement on first principles!

Hmm - that drawing would really screw things up for me, as I use the complex representation so much - with Y representing the imaginary part the quadrants are then as below:

2 | 1
3 | 4

But I entirely agree the first principles bit. If you use it a little, it reinforces the understanding. If you use it a lot, you still have the understanding, but don't need to go through the mechanics.

Now that you mention SOHCAHTOA, I remember it (so obviously it is taught here in the USofA) , but I clearly do not use it on a daily basis, although I do use trig on a daily basis. I use trig so frequently that I just remember the definitions (sin=opp/hyp etc.), with no mental crutches. On the other hand, I didn't even remember the quadrant thing: I work mostly with drawings, and simply change my reference around so I always use acute angles. If I'm working with anything of a wave nature, the wave itself shows me the polarity.

Dick

[quote] I wonder if young people today get any grounding in "normal" tech-drawing.[/quote]

I can tell you for sure that normal pencil on paper is just glossed over in most of the drafting and design courses in may area at least. Most of the instructors don't have the slightest clue about it! At best they have a fair bit of knowledge in the software they are teaching, but that is as far as it goes for most of them.

Some Old Hags Can't Always Hide Their Old Age

Brilliant ! LMAO

I always thought SOHCAHTOA was an American indian, perhaps a relative of Sacajawea.

Dick

Apologies ACCEPTED!!!

"It isn't what you have that counts, it's what you do with it!"

I LIKE THAT!!!

Here's the story behind my signature:

Years ago, when I was young, back in ancient history, my family liked to play dominoes and another domino game called "Moon." One day my oldest brother, my best friend and I were playing Moon. My brother dominated the game early, and started to brag about it, so my friend and I teamed up and I helped my friend beat him.
Then in '98 & '99, I worked at an auto parts warehouse where some of the employees liked to play dominoes in the breakroom during our lunch hour. One day a guy looked at the hand he just drew and made a noise indicating his disgust at drawing what he thought was a bad hand. Remembering the earlier incident, I said, "It aint whatcha got that counts, it's whatcha do with it!" He called me a "history teacher." I polished up the language to fit the (mostly) professional tone of CR4.

Speaking of professional tone, I must commend Randall and the others who came up with 3D approaches to this challenge. That reflects thinking that may not be "out of the box", but definitely "off the page." This has inspred me to create a 3D model or two that incorporates the geometry that is the subject of this challenge. I'll try to post them in a day or two.

" Years ago, when I was young, back in ancient history, my family liked to play dominoes and another domino game called "Moon."

I just had to know about Moon so I found it here.

Dominoe Game Called "MOON"

Also a popular recent game is Mexican Train Dominoes.

Mexican Train

"Speaking of professional tone, I must commend Randall and the others who came up with 3D approaches to this challenge. That reflects thinking that may not be "out of the box", but definitely "off the page." This has inspred me to create a 3D model or two that incorporates the geometry that is the subject of this challenge. I'll try to post them in a day or two."

For anyone wondering if this has a "real world" application:

I created this in AutoCAD 2007 using the 3D Modeling environment. I created the teeth by the method given in the official answer. I drew the ring of circles with n = 50 and r = .125 inch, then trimmed the outer edges of the circles to form the teeth. I combined the resultant arcs into a polyline. This was necessary to form a solid extrusion. Before extruding, I drew a 3/4 inch diameter circle for the center hole. I extruded both the polyline and the circle .500 inch, then subtracted the circle to form the hole. I finished by drawing a rectangle for the keyway, converted it into a polyline, then extruded and subtracted it.
This was my first time using ACAD 2007 for 3D modeling. I began in the 3D world using Mechanical Desktop, and have done some in Inventor. Between MDT and Inventor, I prefer MDT because it works more like ACAD, and it allows me to use the grips I'm used to using!

Also, I have to commend Andyman for coming up with a workable alternative to the official solution. I may have more commendations to hand out later. As far as real prizes, well, I remember that Marvel Comics back in the 1960's and 70's used to hand out "No Prizes"...

Nice drawing. Is it going to get made up for some purpose ? If it's a gear wheel, would the sharp edges of the teeth need smoothing off ? Don't know if anybody here has used it, but there's something called eMachineShop. I think it's aimed more at prototype part production. You can download all the stuff for 3D design/material spec/costing and so on. You then submit it and a formed part gets mailed to you. Not really my scene, but it may be of general interest. I suspect the CAD is limited and the cost expensive, but it may be of use to hobby type projects. I'd be interested to hear how those in the know rate it.

Perhaps you may need to use it in Project Sooty...

It has possibilities, though I'd have to avoid loss if milling some kind of Sooty-resin. She's odds on to have some kind of BBQ, with later incorporation into some kind of matrix material. My favoured idea is to end up with some kind of monolithic type thing. Either like 2001, of the cover of Zeps album 'Presence'. The 2001 idea would have to be scaled down a little.

2001? Did I miss something? <-is that a baffled smilie?

Hmm...I'll have to do some more thinking, I was working on having Sooty as recognisable in her afterlife...you could incorporate her into your kayak/sailboat/car/bicycle as part of a component...

Noooooooooooo.....

Have her cast in a flexible medium and you can use her to make a cat's cradle!!

I'll get me coat....

I may have to scavange a few extra cats to bulk things up. Nah, the table-top Zep idea is starting to excite me ! A lovingly crafted mould, some resin, a bit of colour additive....

Is that you behind the screen, mepho?

OMG, what have I done ! Silk can be very sheer, but I just never knew how complex 2001 was. I only just realized how pleased both the guys in those pictures look. The table ornament is starting to look safer, on the other hand... I'm sure I was manipulated into all this.

I just plugged in 50 teeth for the software I mentioned, Couldn't be bothered fine tuning it with the keying/scale/3D etc, but it shows the general idea.

What I drew was a sprocket for a chain drive. I have seen chain drives used mostly on bicycles, engine timing, 4WD transfer cases, and conveyor systems, and IIRC, the teeth are sometimes sharp.

It's not going to be a production part. I drew it for three reasons: 1) to show the geometry of a ring of circles could have a practical application, 2) I'm not working as a drafter right now, and I need to keep my skills up for when I do get back into it, and 3) I used the AutoCAD 2007 3D modeling environment to learn about it.

I worked on a project a few years ago where the models I created were used in a prototyping machine. I created the models in Mechanical Desktop, a program that uses AutoCAD as its core, but has tools added for 3D parameterization. I saved the models as stereolithography (.STL) files. The prototyping machine turned those files into parts made of resin. That was the first time I got to see something tangible made from something I drew.

Maybe you can have Sooty scanned into a stereolithography file, and then you can have as many replicas of him as you want, or can afford.

Interesting. I think they use some kind of photopolymer (?) and the kit is probably quite pricey, but I'll keep it in mind. Mixing a bit of Sooty in the polymer/resin stuff might mess up the process a bit, though I'd have to check up. More than likely Sooty is going to be a hand crafted kitchen-sink type job.

All that CAD looks like fun, but this dog is getting a bit old (well probably more like lazy) for new tricks. I find it more fun to figure out how to do stuff in my head or with a bit of paper, so you question has been fun. Trying to visualize 3D geometry is good brain exercise. I'm intrigued about what you have in mind for another similar problem. As somebody (sorry ,forgot who you are) said in this thread, CAD is so ubiquitous, it makes me wonder how recent graduates would cope without a computer. I'm not exactly a Luddite, but maybe we are beyond a point of no return - basic skills get sacrificed because people have to keep pace with technology. Sort of like relying on computer designed/built chips that become essential and nobody knows how they work. Perhaps I'll skulk off to live on some remote Island .

I think photopolymer was the first technique to be developed, and it's certainly still in use. Originally developed at IBM, I think, but I wouldn't swear to it. These days they use a range of techniques for different materials. They are mostly laser-driven, but electron-beam methods are used for titanium and I believe tungsten. I believe there are even methods that use ink-jet printing, using a soluble material for the bits they don't want to keep.

Fyz

Hi Kris

'Old' is as much a state of mind as it is a condition of the body. I clearly remember when I was a kid, that a person of 65 years age was really old; I'm past that age now, and don't consider myself old, much less 'really old'. I do know quite a few people born the same general time as myself, who ARE 'old'.

Among the things that I believe help keep one young is learning new things. One of the things I've got to learn soon is 3D drafting - I only know the barest fundamentals. I did study perspective way back when, but I have no idea how you go about true 3D on paper!

BTW I'm guessing 'Sooty' must be a comic strip character. If not, please educate me!

Dick

In the UK, sooty is quite a common name for a long-haired black cat. These animals are commonly dearly beloved of the families that they own; sometimes the families become so distressed when their owners leave them alone in the house that they create images to persuade themselves they have not been abandoned.

(Kris - did I get the long-haired bit right).

A different Sooty is a small honey-coloured bear glove puppet with a dog 'friend' called sweep - but that is to trivialise matters, as their joint emotional age is about 3.

Fyz

P.S. I agree about the age thing - my father seemed old at 45, but in reality was still young into his 90s, at which point he learned to use a computer in case his handwriting later became too shaky to read (it did, as did his drawing - but because he'd learned to use the computer, he was still able to produce publishable work)

You clearly understand cats very well Fyz. Just for general edification and amusement. Sooty is a she, and has medium length hair. Whilst jet-black in colour, the hair/fur takes on an alarmingly ginger tinge when she lounges in sunlight too long. A photo will merge sometime, but she has developed a knack of seeing me approach with a camera and moving. Without the eyes showing it would be hard to tell what was in the picture.

The puppet Sooty will have ER in tears of nostalgia. Without question Sweep was the better puppet. It all went downhill with Matthew Corbett though.

On your PS: The way in which computers can enable people with disabling conditions to carry on living full lives probably outweighs any negatives that I could see. Even stuff like Second-Life has it's uses in that respect. Blind people who use computers amaze me. I'm sure you can get Braille interfaces, but most seem to rely on memory skills in the same way that some Chess players can

Hi Dick,

Totally agree with that whole notion of age being a state of mind. I'm always ambiguous about my age (well most things I guess) for that very reason. The press over hear is constantly full of amazing things that very old folk get up to. It's possibly a result of people living longer - society can't just dump old folk in 'homes' so easily and we all know we could be in the same age-group one day. A new thread on 'amazing old people' would turn up some interesting stuff. I've noticed a lot of post-pension age people getting to grips with computers/internet over the past few years (and doing so very well). One of the UKs last 7 WW1 soldiers died recently at about 107 years old (approx figures from memory) and he looked fairly with-it (which is probably why he lived so long).

I'm not sure you can truly depict 3D by any method apart from a physical structure. I'll be taking a look at CAD and 3D in particular, though I'm not sure to what purpose. What I mean is, does it still present challenges once you've learned to use a decent package.

Kris

3D CAD will rotate the object just as if you had it on a turntable or a spit. You lose the ability to handle your model, but on the other hand you can choose viewpoints and magnifications that you could never achieve in practice. Than you can have a prrrrototype made and see what you've missed (usually some feature of the situation in which it will be used).

Hi Kris

I'm afraid the living longer thing is commonly a problem. My mom is 98, but hasn't done anything constructive in quite a few years. I sure hope I don't live long enough to be in that condition...

I'm about to find out more about those CAD challenges. I've been a Mac guy since '84, but am now typing on my shiny new Intel MacBook Pro, which I just got so I can run the Windows software our suppliers and customers use, and for the motion controller software that I use. I have used VectorWorks and its predecessor MiniCad for nearly 20 years, but it seems that the majority of the people I work with have switched to SolidWorks, so I'm planning to learn that.

As to whether it continues to present challenges, I suppose that depends on what you do with it. I'm mostly designing parts for turbine engines, and the fixtures to hold those parts, as well as automated machines to make them, so I have plenty of challenges.

For me, the greatest advantages of CAD include the ability to use very high precision ( I frequently use 6 digits, so there will be no rounding error when a part is made to 4), the ability to replicate, both in circular and linear arrays (I do a lot of toothed wheels with very special teeth), the ability to use color and layers (so I can see how different parts fit, or don't), and the ability to almost instantly share drawings worldwide.

Dick

Anything that still works is not totally obosolete. If you need to drive from New York to Los Angeles, a Model T will get you there. However, a Cadillac will be more comfortable and get you there faster.

The school where I learned drafting taught me to draw with pen and paper. They did that to make sure their students learned drafting. You can use CAD programs for things that have nothing to do with drafting. I read an article years ago that said some outfits used AutoCAD for graphics.

CAD's biggest advantage is that you can revise drawings or fix mistakes faster. But sometimes a rough sketch can help you visualize a concept quickly.

I can see your reasoning about the cars, but I'd like to try one of these. Or perhaps.

You should have been at Silverstone over the weekend - lots and lots of that sort of thing - racing. It was brilliant. And the sun shone.

It was a shame the Monzanpolis got past the ERA in the tailend traffic, but at least the E-Types beat the Cobras!

<ER is pleased that the glow-in-the-dark aspect of her sunburn has faded>

Waaah.

E-types ! drooool. British racing Green mmmm..... new pants please

< don't go near David Dickinson again>

No BRG - the winner was in white! There was very orange No. 19 AC Cobra...came 4th I believe.

We were trying to get my boss to enter that (he's got a jag that qualifies)...and he used to work at NP...

The car parks were as interesting as the display stands...

You're a 'Blair-babe', and Prescott was a Nurse !?!

Maybe it's worse and you missed a 'C'.....

I need some meds. Fast.

Wash your mouth out with this nice bar of carbolic soap! <very angry smilie>

I was a Thatcher-Teen, definitely not a Blair-Babe! It is to our family's everlasting shame that the first of the next generation was born on the day TB came to power .

And just because you have a thing about women in uniforms, stop imagining me as a meter maid!! And don't call me Rita!

I gargle sulpher.

Now I don't know whether to reach for a calculator, or check wardrobe.

I knew I shouldn't have deleted the "nice bar of rose scented soap" phrase - here, cop a mouthful of this!

If it's soap on a rope you might yank it back, and I'd loose me fangs ! Even worse, they might chip the Avocado bathroom suite.

Kris, What you need is one of these machines from University of Bath - I remember reading an article where they were giving away the machines for nothing, so the only costs were the running costs. Sounds just like what you need for Sooty.

Re: the puppet...even at 4 and 5 years of age, I thought the whole set up was condescending! But then, I was watching Crown Court at that age...and I wrote to Ken Follet a little while back when I found out that he's written for the show.

Luurv that link. Somehow he went back in time having nicked my idea ! I started a thread a while back ('march of the machines' or something like that).

All those puppets were idiots, but Sweep was cool. Admittedly Corbett & son were a waste of space. I remember Crown Court, but I'm not saying at what age ! Have you read 'Pillars of the Earth' *? I really enjoyed it's panoramic sweep. I rarely do fiction reading these days (my own life is surreal enough )

* there's another writer with a similar name I think.

For general background, here is Sooty;

Looks like the one from across the road that I hiss at (I'm fluent in Cat...lost a lot of my Dog from lack of use...mind you, the Cat's going now as current co-habitee doesn't chat as much as Kit did)

My mistake - I should have said James Follett. BBC7 have been running a number of his books (Earthsearch is on at the moment) and I checked out his website, spotted the CC ref and emailed him. Got a really nice reply.

Neighbours eah !

That 'Pillars' is still a good read - architecture and stuff. I'll have to get up to speed on the other. Damn phone keeps ringing - back laters.

In that case, its easy: the angle between circles is 360°/n, so the angle between the center and the tangent points is half that, or 180°/n. The radius r of one circle is the opposite side of a right triangle whose hypotenuse R (R=r/sin(180°/n) is the distance from the center of the ring to the center of one circle.

So in CAD, create one circle of radius r at the origin, move it up r/sin(180°/n), and duplicate it n-1 times in a circular array with an angular separation of 360°/n.

Dick

No more than three circles of the same radii can be mutually tangent. The question erroneously implies otherwise. PTHHHT!

Try 3 dimensions

"No more than three circles of the same radii can be mutually tangent. The question erroneously implies otherwise. PTHHHT!"

Only if you live in a two dimensional world.

It's way past time to move into the 3-D world of the 21st Century.

See above posts!

go by step

This has gotten really abstract guys! Use the features of the CAD software. Assuming that this is in the 2D plane (and that the circles are all tangent to each other) the array of circles must be 3 circles. It can be done using 3 AutoCAD commands

For AutoCAD (enable osnap QUADRANT AND TANGENT);

1) Draw a circle of 'n' radius

2) 'CO' COPY the circle and place it (suggest using quadrant osnap) next to itself.

3) Draw the 3rd circle using TTR (TanTanRadius). Use circle 1 and circle 2 for the tangent points. Use 'n' for the radius.

Simple!

Just following on from earlier post; the quest did not say anything about the circles having to be in a polar array around a common point. The circles could arranged in a 'honeycomb' type array.

Take my earlier example and continue to draw circles tangent to adjacent circles using CIRCLE TTR

To draw a ring of tangent circles do the following in AutoCAD;

1. Draw a horizontal construct line
2. Draw a construct line of angle (360/'n'). Intersect the horizontal line with this line
3. Draw a circle using TTR inside the 2 lines using 'r' for the radius.
4. Polar Array the circle using the intesection as the center point. Array the circle 'n' number of times within 360°

.

Nice demonstration.

How about a sphere of tangent circles?

You mean a ball?

Wouldn't that be a regular solid with a circle for each face?

Would it be possible to make such a solid? A bucky ball requires hexagons and pentagons...so wouldn't you need two sizes of circle to make a sphere from circles? Or do the included circles (i.e. the ones inside the hexagons and pentagons) turn out to be the same size, with just the gaps determining the ~agon size and shape?

Who succeeded to B-F's throne?