hopp@nbs-amrf.UUCP (Ted Hopp) (03/12/85)
> My favorite is: > Why are manhole covers round? > There are two answers. I can think of at least three answers: 1. Because they aren't any other shape. 2. Because manholes are round. 3. So that manholes can be round. Do I get the job? -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp
krs@amdahl.UUCP (Kris Stephens) (03/15/85)
> > My favorite is: > > Why are manhole covers round? > > There are two answers. > > I can think of at least three answers: I always thought it was because it's the only shape that can't fall through its own hole (assumption: beveled edges). -- Kris Stephens (408-746-6047) {whatever}!amdahl!krs [The opinions expressed above are mine, solely, and do not ] [necessarily reflect the opinions or policies of Amdahl Corp. ]
ndiamond@watdaisy.UUCP (Norman Diamond) (03/15/85)
(Note that this follow-up is not posted to net.jokes, only net.puzzle. Perhaps it belongs in net.flame.) > > Why are manhole covers round? > I can think of at least three answers: > 1. Because they aren't any other shape. > 2. Because manholes are round. > 3. So that manholes can be round. Answer 1 is false; I have seen square manhole covers. There is of course at least one valid answer (which has already been posted), and these answers 2 and 3 demonstrate how an un-clever person would rather be an asshole than respect those who figure it out (or who try). Yes, this qualifies him for a job (flushing toilets), but probably brings him a much better job (marketing, or mis-managing engineering departments, etc., using his talents). -- Norman Diamond UUCP: {decvax|utzoo|ihnp4|allegra}!watmath!watdaisy!ndiamond CSNET: ndiamond%watdaisy@waterloo.csnet ARPA: ndiamond%watdaisy%waterloo.csnet@csnet-relay.arpa "Opinions are those of the keyboard, and do not reflect on me or higher-ups."
hopp@nbs-amrf.UUCP (Ted Hopp) (03/18/85)
> (Note that this follow-up is not posted to net.jokes, only net.puzzle. > Perhaps it belongs in net.flame.) > > > Why are manhole covers round? > > I can think of at least three answers: > > 1. Because they aren't any other shape. > > 2. Because manholes are round. > > 3. So that manholes can be round. > Answer 1 is false; I have seen square manhole covers. > > There is of course at least one valid answer (which has already been > posted), and these answers 2 and 3 demonstrate how an un-clever person > would rather be an asshole than respect those who figure it out (or > who try). Yes, this qualifies him for a job (flushing toilets), but > probably brings him a much better job (marketing, or mis-managing > engineering departments, etc., using his talents). > > -- > > Norman Diamond As the "asshole" that seems to irritate Mr. Diamond so much, I feel I should respond, although I'm not sure why. The original question was posted to net.jokes as well as net.puzzle, so I answered it in the spirit of net.jokes. I don't see how that shows a lack of respect for those who approach it as a puzzle, or why they (or perhaps just you, Mr. Diamond) should feel denigrated. As a point of logic, if there are square manholes, how can there be ANY valid answer as to why manholes are round? My answer 1 was a variation on one of the Baron von Munchousen stories. ("Where are we?" "In Bavaria." "How do you know?" "Can you say we are anywhere else?" "No." "If we are not anywhere else, we are in Bavaria.") As a point of information, the original poster of the question admitted on the net that one of the answers he was looking for was my answer 3. (I guess he is an asshole, too.:-) As a further point of information, what is this valid answer that was posted to the net? If it is that a round manhole is the only shape that will prevent it from falling into the hole, it has also been pointed out on the net that this is false. There is at least one infinite set of simple closed curves that have this property - the curves of constant diameter. An example of a curve of constant diameter that is not a circle is the rotor of a Wankel engine. Also, why doesn't a manhole cover (of any shape, but let's stick to round ones) fall into the manhole? It is because there is either a ledge on which it rests or the opening is beveled. In either case, I claim that all regular polygons of sufficiently high order approximate a circle closely enough that they will not fall into the hole, either. Obviously, not falling into the hole cannot be why (i.e., the cause that) manholes are round, only an effect of them being round. As a point of personal preference, Mr. Diamond, I offer two more answers that, judging from your reaction so far, should really make you see red: 4. [Round] manhole covers are round so that workmen can move them easily by rolling them. And, since you refer to my managerial talents, Mr. Diamond: 5. Manhole covers are round because it is cheaper to machine a round shape than any other shape. I suggest that your posting didn't belong in net.jokes, net.puzzle, or net.flame. It belonged in net.knee.jerk.reactions. -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp
leeper@ahutb.UUCP (m.r.leeper) (03/19/85)
REFERENCES: <462@nbs-amrf.UUCP>, <1282@amdahl.UUCP> Curves of constant breadth came up during WWII. The British were trying to mill hulls of submarines to have perfectly circular cross-sections. They tried rolling molten cylinders between parallel forming sheets, much like you would roll clay between your hands to make a solid cylinder. The problem was they were not getting circular cross-sections. They eventually discovered that the process gives you only a constant breadth curve, not a circle. The triangle described elsewhere in a response is called a Rouloux Triangle. One of its applications is in a special drill bit that cuts square holes. Placed inside a square frame, one side of which is the length of the breadth of the triangle, a Rouloux shaped drill bit can be made to follow the edges of the square. (It is amazing how many interesting things you can learn from one really good high school math teacher!) Mark Leeper ...ihnp4!ahutb!leeper
ndiamond@watdaisy.UUCP (Norman Diamond) (03/19/85)
> Placed inside a square frame, one side of which is the length of the breadth > of the triangle, a Rouloux shaped drill bit can be made to follow the > edges of the square. > Mark Leeper Doesn't that produce a "square" with rounded corners? Doesn't the drill bit have to be exactly triangular to produce an exact square? -- Norman Diamond UUCP: {decvax|utzoo|ihnp4|allegra}!watmath!watdaisy!ndiamond CSNET: ndiamond%watdaisy@waterloo.csnet ARPA: ndiamond%watdaisy%waterloo.csnet@csnet-relay.arpa "Opinions are those of the keyboard, and do not reflect on me or higher-ups."
gjk@talcott.UUCP (Greg Kuperberg) (03/20/85)
>> Placed inside a square frame, one side of which is the length of the breadth >> of the triangle, a Rouloux shaped drill bit can be made to follow the >> edges of the square. >> Mark Leeper > >Doesn't that produce a "square" with rounded corners? >Doesn't the drill bit have to be exactly triangular to produce >an exact square? ... > Norman Diamond Nope. Apparantly, the Rouloux drill bit has 90 degree corners. This is just the right angle for fitting in the corner of a square; any other angle (such as 60 degrees, as you suggest) would make the drill bit hit the corner of the frame with a lot of force; the contraption would wear down quickly. --- Greg Kuperberg harvard!talcott!gjk "No Marxist can deny that the interests of socialism are higher than the interests of the right of nations to self-determination." -Lenin, 1918
ndiamond@watdaisy.UUCP (Norman Diamond) (03/20/85)
> (Ted Hopp writes) > The original question was posted to net.jokes as well as net.puzzle, so > I answered it in the spirit of net.jokes. I'm sorry; I thought the puzzle was only posted to net.puzzle, and that you had added net.jokes to your answer. > As a point of logic, if there are square manholes, how can there be ANY > valid answer as to why manholes are round? Uh, digressing back to technical correctness, there is a valid answer why manholes SHOULD be round, == the valid answer why MOST manholes ARE round. > As a point of information, the original poster of the question admitted > on the net that one of the answers he was looking for was my answer 3. Yes, I noticed that in his answer too, and its sensibility is quite appropriate for net.jokes. Again, I apologize for that mis-interpretation. > ... it has also been pointed out on the net that this is false. There is > at least one infinite set of simple closed curves that have this property > - the curves of constant diameter. Also true, but this was not considered by the original poster, nor by you, nor by me, so it is kind of irrelevant. > Also, why doesn't a manhole cover (of any shape, but let's stick to round > ones) fall into the manhole? It is because there is either a ledge on > which it rests or the opening is beveled. Also true and irrelevant... > In either case, I claim that all regular polygons of sufficiently high > order approximate a circle closely enough that they will not fall into > the hole, either. Digressing again to technical matters -- not if the bevel is sufficiently small (depending somewhat on the order of the polygon). > As a point of personal preference, Mr. Diamond, I offer two more answers > that, judging from your reaction so far, should really make you see red: > > 4. [Round] manhole covers are round so that workmen can move > them easily by rolling them. I did regard that answer as a joke (even not knowing that the original puzzle had been half-intended as one). Although I was not impressed with the quality of that joke, I remained silent because I am well aware of differences in taste -- that kind of joke surely appeals to some people, and they have a right to share it. > And, since you refer to my managerial talents, Mr. Diamond: I don't know anything about your managerial talents. I have known the "talents" of 90% of the managers I have had to work for. They were more capable of insulting people's discussions of problems and answers they disliked, than of understanding what the problems and answers really were. > 5. Manhole covers are round because it is cheaper to machine > a round shape than any other shape. Oh! I believe you ... but then have to wonder, why are so many other manufactured objects NOT round .... > I suggest that your posting didn't belong in net.jokes, net.puzzle, or > net.flame. It belonged in net.knee.jerk.reactions. Yes, net.knee.jerk.reactions would have been appropriate. Why would net.flame have been inappropriate? Net.misinterpretation would have been appropriate too. -- Norman Diamond UUCP: {decvax|utzoo|ihnp4|allegra}!watmath!watdaisy!ndiamond CSNET: ndiamond%watdaisy@waterloo.csnet ARPA: ndiamond%watdaisy%waterloo.csnet@csnet-relay.arpa "Opinions are those of the keyboard, and do not reflect on me or higher-ups."
doug@terak.UUCP (Doug Pardee) (03/21/85)
Reason # 6: So that it can be installed in any orientation?
--
Doug Pardee -- Terak Corp. -- !{hao,ihnp4,decvax}!noao!terak!dougleeper@ahutb.UUCP (m.r.leeper) (03/21/85)
REFERENCES: <462@nbs-amrf.UUCP>, <1282@amdahl.UUCP> <564@ahutb.UUCP>, <7093@watdaisy.UUCP> >> Placed inside a square frame, one side of which is the >>length of the breadth of the triangle, a Rouloux shaped >>drill bit can be made to follow the edges of the square. >> Mark Leeper > >Doesn't that produce a "square" with rounded corners? >Doesn't the drill bit have to be exactly triangular to >produce an exact square? It didn't, though I cannot reproduce in my mind exactly how it did it since a Rouloux triangle has a vertex angle of 120 degrees, so it shouldn't be able to fit into a square corner. If it had a 90 degree vertex angle it seems it would work but not with 120. Oh well! Mark Leeper ...ihnp4!ahutb!leeper
ph@wudma.UUCP (03/21/85)
> > Placed inside a square frame, one side of which is the length of the breadth > > of the triangle, a Rouloux shaped drill bit can be made to follow the > > edges of the square. > > Mark Leeper > > Doesn't that produce a "square" with rounded corners? > Doesn't the drill bit have to be exactly triangular to produce an exact square? > Norman Diamond Yes, it does, but using an exactly triangular bit doesn't help; it only allows the bit to jiggle around more. Incidentally, any of you mechanical types out there care to discourse on the problems involved in driving the bit when it doesn't rotate around a fixed axis? I've always wondered about how that was done. --pH /* * "Pardon me for breathing, which I don't do anyway so I don't * know why I bother apologising for it, oh GOD I'm so depressed." */
ee163acp@sdcc13.UUCP (DARIN JOHNSON) (03/22/85)
> > Placed inside a square frame, one side of which is the length of the breadth > > of the triangle, a Rouloux shaped drill bit can be made to follow the > > edges of the square. > > Mark Leeper > > Doesn't that produce a "square" with rounded corners? > Doesn't the drill bit have to be exactly triangular to produce an exact square? Yes, but that way you get a little bit of bite for those square screws !!! Darin Johnson
leeper@ahutb.UUCP (m.r.leeper) (03/22/85)
REFERENCES: <462@nbs-amrf.UUCP>, <1282@amdahl.UUCP> <564@ahutb.UUCP> <7093@watdaisy.UUCP>, <371@talcott.UUCP> On whether a Rouloux triangle can really cut I square hole as I previously claimed. >Nope. Apparantly, the Rouloux drill bit has 90 degree >corners. This is just the right angle for fitting in the >corner of a square; any other angle (such as 60 degrees, as >you suggest) would make the drill bit hit the corner of the >frame with a lot of force; the contraption would wear down >quickly. --- That was my original reasoning. I still believe it to be the way it was described to me. Just after I published my original statement I did the geometry and discovered to my embarrassment that the true Rouloux triangle has 120 degree corners. Unless my geometry is wrong. Let me give my argument, I could be making an error. To construct a Rouloux triangle start with an equilateral triangle with vertices A, B, and C. Now draw the short arc from A to B with center C, from A to C with center B, and from B to C with center A. Now how do we measure the vertex angle at B. Let c be the line tangent to the arc from A to B with center c. Line segment BC must be perpendicular to c since it is tangent to a circle with center c, namely the continuation of the arc from A to B. Angle ABC is 60 degrees, since it is a corner of an equilateral triangle. This makes the acute angle formed by segment AB and c to be 30 degrees. Hence the whole vertex angle at B is 30 + 60 + 30 degrees. That's 120 degrees. Mark Leeper ...ihnp4!ahutb!leeper
slb@druxq.UUCP (Sue Brezden) (03/22/85)
Since curves of constant diameter have been mentioned...
Poul Anderson wrote a story involving those curves. Seems
a space ship is marooned on an undeveloped planet. They
need to move a very heavy engine from a storage place to
their ship. (The engine had been placed there earlier to
help out in just such an emergency. However, they crashed
a few hundred miles away from the storage place.)
Unfortunately, the culture on the planet believes that the
circle is holy, and forbids its use. They need a substitute
for round wheels--and find it in a triangular curve of constant
diameter.
Unfortunately, I cannot remember the title of the story. I
recommend it, however.
Sue Brezden
drutx!druxq!slb
"'Well, master, we're in a fix and no mistake,' said Sam"ndiamond@watdaisy.UUCP (Norman Diamond) (03/22/85)
> ... I feel I should respond, although I'm not sure why. > > The original question was posted to net.jokes as well as net.puzzle ... My combination of apology, replies, and rebuttals are unchanged from when I replied to the first posting of the referenced article. -- Norman Diamond
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (03/22/85)
> ... any of you mechanical types out there care to discourse on the > problems involved in driving the bit when it doesn't rotate > around a fixed axis? Use an eccentric chuck and a square template.
ee163acp@sdcc13.UUCP (DARIN JOHNSON) (03/22/85)
> Reason # 6: So that it can be installed in any orientation? > -- > Doug Pardee -- Terak Corp. -- !{hao,ihnp4,decvax}!noao!terak!doug I like this reason, it eliminates all training involved to take out or replace a manhole cover!!
bob@vaxwaller.UUCP (Bob Palin) (03/27/85)
> > > > > Why are manhole covers round? > > > I can think of at least three answers: > > > 1. Because they aren't any other shape. > > > 2. Because manholes are round. > > > 3. So that manholes can be round. > > As a further point of information, what is this valid answer that was > posted to the net? If it is that a round manhole is the only shape that > will prevent it from falling into the hole, it has also been pointed out > on the net that this is false. There is at least one infinite set of > simple closed curves that have this property - the curves of constant > diameter. An example of a curve of constant diameter that is not a > circle is the rotor of a Wankel engine. > > Also, why doesn't a manhole cover (of any shape, but let's stick to round > ones) fall into the manhole? It is because there is either a ledge on which > it rests or the opening is beveled. In either case, I claim that all > regular polygons of sufficiently high order approximate a circle closely > enough that they will not fall into the hole, either. Obviously, not > falling into the hole cannot be why (i.e., the cause that) manholes are > round, only an effect of them being round. > Man holes and their covers are indeed round to prevent the cover falling into the hole, this may be, as pointed out, not the only shape they could be but is the most obvious shape to just about anyone. As for other 'high order regular polygons' working just as well I suppose it depends on what you mean by high order. Certainly no four sided cover will work and it seems likely that you would have to approximate a circle so closely as to be pointless. Was the original question theoretical or practical ? Bob Palin, zehntel!varian!bob
alexis@reed.UUCP (Alexis Dimitriadis) (03/29/85)
>> >> > > > Why are manhole covers round? >> >> Also, why doesn't a manhole cover (of any shape, but let's stick to round >> ones) fall into the manhole? It is because there is either a ledge on which >> it rests or the opening is beveled. In either case, I claim that all >> regular polygons of sufficiently high order approximate a circle closely >> enough that they will not fall into the hole, either. >> >Certainly no four sided cover will work >and it seems likely that you would have to approximate a circle so closely >as to be pointless. Was the original question theoretical or practical ? > >Bob Palin, zehntel!varian!bob (Naturally, net.jokes is an inappropriate place for this discussion, but I find it interesting). Think about what "beveled" means. Yes, even a square cover will not fall in its hole if bevelled enough. (Think of it as essentially upside-down pyramid shaped). Clearly, anything larger number of edges would work better and better. Someone pointed out that you can roll a round cover into place. A round cover can also be dropped in its hole without concern for alignment, unlike any polygonal shape. Besides, has anyone realized that round manhole covers generally cover round manholes? A round manhole (cylinder) has the smallest surface-to volume ratio possible, and is therefore cheaper. (Sewer pipes are also round. Anyone care to speculate on why?). Let me add a plea to restrict future discussion to net.puzzle, and net.manhole.cover. The plea doubles as the obligatory joke, since noone will follow it. Facetiously, alexis PS. The discussion on the Roullaux (sp?) drill was rather interesting. Does anyone know the actual shape of the drill? -- _______________________________________________ alexis @ reed ...ihnp4!{harvard|tektronix}!reed ...decvax!tektronix!reed ...teneron!reed
ron@brl-tgr.ARPA (Ron Natalie <ron>) (04/01/85)
> > Think about what "beveled" means. > Yes, even a square cover will not fall in its hole if bevelled enough. > (Think of it as essentially upside-down pyramid shaped). > Clearly, anything larger number of edges would work better and better. > It's really not beveled. It's that the covers are bigger than the hole. Round covers are cylinders. If you use a square cover, it has to be larger than the diagonal of the hole to prevent it from falling in. -Ron
trb@masscomp.UUCP (Andy Tannenbaum) (04/09/85)
In an innumerable number of articles, many netters write: (I paraphrase) > Manhole covers are round because if they were square, they would > fall into the manholes (assuming a minimal bevel). People have said that the covers would have to be round, or at least many-sided, approaching round, or of some goofy equidiametric non-circular shape or something. I don't quite follow it all. It seems to me that an equilateral triangle cover would serve just as well as a circle, when it comes to keeping the lid from falling in. Of course, there's still the rolling problem, but my point is that there seem to be scads of people posting to the net saying that a circle-like shape is the only choice because of the "falling in problem" and that they're apparently not right. Mr Telephone Man, there's something wrong with my line when I alloc(my baby's number) I get a click every time. Andy Tannenbaum Masscomp Westford, MA (617) 692-6200 x274
trb@masscomp.UUCP (Andy Tannenbaum) (04/09/85)
In article <661@masscomp.UUCP> I, trb@masscomp.UUCP (Andy Tannenbaum) write: > People have said that the covers would have to be round, or at least > many-sided, approaching round, or of some goofy equidiametric > non-circular shape or something. I don't quite follow it all. I should have stopped here... I went on to incorrectly offer the notion that equilateral triangles would would not fall in. Sorry to spew without more forethought. Thanks for not sending me threats upon my yet unborn children. But with sufficient bevel... Andy Tannenbaum Masscomp Westford, MA (617) 692-6200 x274