Second grade math question:

[SlippShodd]

"How many edges does a cone have?"
No, not an ice-cream cone. Think geometric shape.
There's no prize, just an ongoing discussion for the benefit of my 8-year old nephew, who is plenty pi$$ed that his answer was considered wrong by the modern mathematical definitions.

mike

[Sweetpea]

One???

[Jim]

Are we talking about a three demensional cone? And you ask about 'edges'; edges or sides?

[freebullet]

Um, no prize? Is this a trick or something?

[hithard]

Three

[chsparkman]

As a mathematician, I would say one if we are referring to a classically geometrical definition of a cone.

[theperfessor]

One where the base and the cone intersect. Depending on the definition used, one more for the point on the top if an intersection that forms a point and not just a line is counted.

[MBTcustom]

I'm with the perfessor. What gives?

[TXGunNut]

Another vote for "one".

[swheeler]

another vote for one

[Idaho Mule]

I say one, unless the rules change, then I still say one. JW

[fouronesix]

I'd think one edge and one point. A truncated cone would have two edges and no point (better through something in there about a common bullet nose design :))

[kenyerian]

A cone has one flat face, one curved face, one vertex and one curved edge.
One.

[runfiverun]

a cone will have an infinite number of edges as soon as it makes the 90* turn it becomes an infinite number of measurements the more and finer you measure it.
you can call it one with a straight edge, but measure it microscopically and the number keeps on increasing.

[nvbirdman]

A cone has an open end and a closed end. The open end is where you put the ice cream.

[Edubya]

Answer:
One.

But it is a bit tricky and depends on how you define an edge.
Many use the definition of a boundary of a geometric figure
Please see the link to the math forum at Drexel University.
There is a lengthy discussion of this topic.

A cone has one flat face, one curved face, one vertex and one curved edge.
One.

EW

[Bullshop]

Well I disagree with that answer. For something this importent we should not leave it to chance. We really need to apply for a federal grant to study this in depth enough that we have the conclusive answer. The study would include maping posative terminology as well so no one would mistakenly call a surface and edge.
This just makes my mind spin out of controll. I mean think about the answer given, "1". How is that possible in a three dimentional world? If there is an edge at all it would have to have depth and if it has depth the edge would have to have an inner and an outer edge. We really need to put our best available minds to work on something as importent as this. bout $100,000,000.00 aughta do it. The world will be a better place. Do it for the children.

[Rooster]

Surely ballistic testing is in order!

[SlippShodd]

I appreciate all of your responses, and I will pass them along to my nephew, his father, and maybe the state board of education. By and large we all agree that the logical answer would be "one", considering (yes, Jim) a 3-D cone. On the other hand, according to his teacher, the correct answer is "zero." She was sympathetic when my BIL confronted her on the subject, and seemed to be willing to agree, however was bound by whatever mathematical definitions she was provided for instructional use. I'll see if I can get a clear explanation; the one I heard was from a fuming father and filled with vulgarity, but it almost seemed to rely on the presence of right angles, contradicting another correct answer in which a triangle possesses 3 edges.
It was the only question on the test that my nephew got wrong and he was thoroughly peeved. He is quite bright, very opinionated, and quite capable of mounting his own defense. He's also a budding gun crank, forever pleading his case to start loading his own ammo and casting his own boolits. This is him during a camping trip last summer, destroying clay pigeons with my M&P 15-22.
66252
Later he got some trigger time on the .223 and my Walther PP. He's 4'7" and a buck-twenty -- he's 8 years old! Already a force to be reckoned with.
Such is the state of modern public education. Next they'll try to tell him the world is round.
>shudder<

mike

[missionary5155]

Good morning
If I am viewing a cone I see the disassembled planchet.. I work/play with sheetmetal. I recon some others would turn one out of a solid but I never yet have had a lathe in my posession.
Four years of mechanical drafting in high school and for life all I see is the parts and how to make them.
Your son is far better off thinking about trigger control than having to wonder how many edges any object has.
Mike in Peru

[smokeywolf]

Your nephew's teacher is operating under the theory that a face is always flat and a surface not. According to this line of thinking, you can only have an edge where two faces meet; not where a face and a surface meet. Ergo, neither a cone nor a cylinder have edges.

By the way, the definition of a face and a surface will differ according to who the mathematician is, that is writing the paper.

smokeywolf

[Harter66]

Not being a nuclear phd ..... my 1st impulse was 1 , however an open cone would not have a "junction" to a flat face/plane. Which in lay terms leaves none , it is circular an comes to a point an has ,as an open cone no face/plane junction. Infinety is also arguable as a circle is made of an infinate number if intersecting planes and an open cone must have a rim on its open end there for an infinate x3 number of inter secting planes,if it does not then it is only a 2 dimsional figure and there fore not a cone .

I think i just made my own head hurt.

[Bullshop]

I have been thinking on this and decided the correct answer has to be 2.
This should proov it. Draw a straight line on a piece of paper. How many edges does it have. In a three-d view it would have 12 edges. I wont even go 3-d for this just flat. So the flat line has how many edges? The answer is 4. One edge on every side top, bottom, right and left side. Now take the line and bend it into a circle. When in a complete circle the top and bottom edges are eliminated becoming a continuous line. That still leaves two edges of the same line, the right and left side. The correct answer then should be 2 not 1.
Have him deminstraight to the teacher the proof cant be denied.

[Bullshop]

I have been thinking on this and decided the correct answer has to be 2.
This should prove it. Draw a straight line on a piece of paper. How many edges does it have. In a three-d view it would have 12 edges. I wont even go 3-d for this just flat. So the flat line has how many edges? The answer is 4. One edge on every side top, bottom, right and left side. Now take the line and bend it into a circle. When in a complete circle the top and bottom edges are eliminated becoming a continuous line. That still leaves two edges of the same line, the right and left side. The correct answer then should be 2 not 1.
Have him deminstraight to the teacher the proof cant be denied.

[Bullshop]

Ya know I just dont know how this happened, sorry.

[David2011]

If the question didn't specify an open cone or a solid cone then it was an incomplete and therefore invalid question with no possible correct answer. A cone in its mathematical description cannot exist in the real world as points have no dimension. Even an answer to the question is only theoretical.

Being more the practical type, I'm thinking along with Mike in Peru and the majority here. Chuck up a chunk of metal in a lathe and turn a conical shape. At the interface of the curved face and the flat face let the teacher feel the sharp edge and if not careful, cut her finger on it. Then she will know the edge exists. No smoothing it off; you would no longer have a simple cone. The machined part may theoretically have an edge composed of an infinite number of connected points but in reality it has a continuous curved edge. Personally, I think the mathematicians invented points because complex curves are too hard to describe in a manner on they would comprehend.

Back to my coffee. . .

David

[theperfessor]

I'll go with zero also IF the cone does not have a base and the lines that make the surface extend to infinity. This is standard in Euclidean mathematics, which is the form of mathematics most of us were taught in school. There are some definitions for concepts such as points, lines, planes, and other surfaces that are implicitly part of Euclidean mathematics.

Non-Euclidean mathematics include different concepts that seem foreign to most of us, concepts such as parallel lines that intersect at infinity, etc. And yet for some purposes this type of math can solve problems that Eucledian math can't deal with well.

It is all part of how we define concepts such as points, line, infinity, etc. I think the question the teacher asked and the answer given as correct was based on an open cone and edges defined as lines and not points.

I'm NOT a math teacher by the way, so there may be a nuance or two I'm missing here, but essentially the answer is based on the framework and concepts implicit in the type of mathematical system being taught.

[Cap'n Morgan]

Ask your son's teacher what the name of the "edge" of the cone is - since it's not an edge... if she answers "rim", tell her she flunked.

[runfiverun]

mike.
your nephew is about the same size as I was when I learned how to cast boolits.

[Smitty's Retired]

Such is the state of modern public education. Next they'll try to tell him the world is round.
>shudder<

mike

Mike, your quote made me laugh, along with bringing up a memorie.

My oldest Grand Daughter is a senior. Several years ago (6th or 7th grade) she came home from school and came by the house. We would always asked what she did in school that day. In science their teacher had explained how the world being considered round was actually incorrect. That due to gravitational forces, the texture and layers of the plates, along with the expasion and flow of the core, that the earth actually changed shape considering different apex's of it's orbit and the gravitational effects of the sun. Later I laughed and told my wife, now the school is saying the world is not round.

[frkelly74]

Zero would have been my second guess. Assuming that the cone is infinite from a fixed point.

[MtGun44]

One edge.

Bill

[JonB_in_Glencoe]

Zero huh ?

Well, My answer would be two !
in most cases an edge is a side.
a cone has two sides...inside and outside ...lol :)
Jon

[dakotashooter2]

NONE............................................. when filled with black powder an 'lit up"................

[shooter93]

It all depends on what your definition of is......is.

[10x]

Define "edge".
If something has zero edges it does not exlst because it has zero surfaces
A ball has one edge....

[TXGunNut]

Ask the smart teacher how many grains are in a pound.

[SlippShodd]

LOL! I knew I brought this to the right place. I also blew up my Facebook page with this question. As a point of clarification, I apologize for omitting, the example shown on the test was a solid cone with a circular base. His teacher is ruing the day he set foot in her class room.

mike
"depends on what your definition of is is." LOLOL. holy deja vu all over again.

[TCLouis]

ZERO
Point or top is the top, not edge,
Bottom is the base and not an edge.

So, what is the real answer??

[SciFiJim]

The correct answer for the test is the one given in the book that was taught to the class.

It is called "teaching to the test" and encourages rote answers and discourages original thought.

Mistakes are taught along with everything else because "it is in the book".

Teach your nephew to be a subversive by giving the "book" answers and thinking his own thoughts.

[fishin_bum]

Don't blame the teacher she is just following the masses! I think the mathematician is helping Zero balance the budget!

[10x]

The correct answer for the test is the one given in the book that was taught to the class.

It is called "teaching to the test" and encourages rote answers and discourages original thought.

Mistakes are taught along with everything else because "it is in the book".

Teach your nephew to be a subversive by giving the "book" answers and thinking his own thoughts.


edge
/ej/
Noun
The outside limit of an object, area, or surface; a place or part farthest away from the center of something: "a tree at the water's edge".
Verb
Provide with a border or edge: "the pool is edged with paving".
Synonyms
noun. border - brim - verge - brink - margin - lip - fringe
verb. sharpen - whet - grind - hem - border

Depends on the definition of "edge". A ball has one "edge" if edge is considered the surface.
If "edge" is considered a corner or a change in plane then a ball has either zero or infinite edges depending on how one defines a ball.
The edge of a single atom changes as well as the electrons keep moving about the nucleus in the outer shell. There is a concept in physics regarding edge that only works if the electron is considered to be in two or more places at the same time.....

Also there is theoretical edge - a mathematical concept - and there is the edge on a physical object. The simple edge we see on an object will be comprised of a subset of a number of edges at the molecular level as the molecules comprising the object have edges in a number of planes as they bond together.

Once again much depends on the terms used to define "edge".

[Wayne Smith]

If mathematicians cannot agree on the answer it is NOT an appropriate question for a third grade class!

[TheDoctor]

Machine a metal cone, 6 inches in diameter, 1/2 inch tall. Tell the teacher to run her finger around it real quick, and if it doesn't have an edge, it won't cut. Practical definition/example.

[Bullshop]

Machine a metal cone, 6 inches in diameter, 1/2 inch tall. Tell the teacher to run her finger around it real quick, and if it doesn't have an edge, it won't cut. Practical definition/example.

That would have 2 edges.

[fouronesix]

If mathematicians cannot agree on the answer it is NOT an appropriate question for a third grade class!

Now that's the truth!
I thought about it some more and it hints at being one of those trick questions so no one gets a 100. If the teacher says zero edges, then it seem like a convoluted way to test for the concept of infinity (3rd grade level! good grief). Because the only way a cone would have zero edges is if defined purely from the mathematical formula- having a confluence terminus (point) and the two dimensional surface extending to infinity. If it is a three dimensional definition of a finite, solid object (seems the picture in the test showed that- a cone where the surface is bisected by a plane) then I'll stick with one edge. But, what the heck do I know.

[starbits]

Cut a piece of paper into a triangle and ask the teacher to point out the three edges. Then take the paper and roll it up into a cone. Two of the edges disappear into the sides, but the third edge is still there as a circle instead of a straight line. The answer is one edge, the teacher a drone unable to think for herself.

Starbits

[Bullshop]

Now look at that edge under hi magnification, how many edges do you see? And edge would be a 90 degree angle or corner yes? How many?

[blackthorn]

For laughs and giggles--look at of the base of the cone. If the cone is solid there is one (1) edge--the outside! If the cone is hollow there are two (2) edges--the outside and the inside! To me the answer to the original question (in this case) is one (1)! I base this on the post that identified this particular cone as solid. This answer is however predicated on the assumption that the base of a hollow cone has not been "boat-tailed" to the point that it has indeed become a single "edge"! There! This post is now cast bullet "correct" with the refference to "boat-tail". Have a great day!!!

[ASM826]

On the other hand, according to his teacher, the correct answer is "zero."
mike
If I make a cone out of sheet metal and I cut myself on it, what would the teacher say I cut myself on?

[.45Cole]

If I make a cone out of sheet metal and I cut myself on it, what would the teacher say I cut myself on?
Booksmart supplemented with common sense.
Polar Coordinates! r, theta, and phi
Theta range is 0 to 2pi
Phi is some function of theta
r ranges from 0 to (end of range) "end of range'=edge

Assuming source at origion. This is how I (engineer) would construct one , I hope it passes the mathematicians check
Your nephew kept a few people busy here. We got his tail covered.

[bgoff_ak]

two, inside outside...
now can I get my Obama participation award… ice cream and what ever other items im intitled to !

[chsparkman]

Over the years as a math teacher I have come across conflicting definitions from different texts which can be very frustrating when trying to be as correct as possible for the kids. This might be one of those situations, and as long as it is not a right or wrong question on a test for which a grade depends, then it's a good question, if only to create the kind of thought and discussion we have seen on this thread.

I'm looking forward to the end of another school year so I can spend summer days casting or shooting.

[felix]

Have you ever seen a math challenge between several PHDs? It can go on for weeks, especially if the "concept" deals with the math field of "topology". It really boils down, in practical terms for us, to the back-and-forth conversion between two languages, such as math and English. Mental telepathy is the only answer for immediate conversion, but the Lord kinda' outlawed that back when the races (languages) were instantly made. ... felix

[Superfly]

I just want to know what kind of Ice cream this cone has in it??????

[427smith]

a ball has a side only one side. no edges. if there was a circle with infinite radius are we on the inside or outside. just for thought.

[bgoff_ak]

I just want to know what kind of Ice cream this cone has in it??????

Its government ice cream flavor, it will come in that brown beige color that every post building is painted. Be slightingly unappealing and barely palatable having a shelf life of no less than 10 years ( under proper storage conditions ) and will cost the government 10 times what you can buy the same ice cream for. Care for a scoop ?

[SlippShodd]

Its government ice cream flavor, it will come in that brown beige color that every post building is painted. Be slightingly unappealing and barely palatable having a shelf life of no less than 10 years ( under proper storage conditions ) and will cost the government 10 times what you can buy the same ice cream for. Care for a scoop ?

He's only 8 years old. I'm not introducing him to George Orwell yet.

mike

[runfiverun]

I think I was eight or nine when I read 1984.
read lord of the flies and lord of the rings right about then too.

[bgoff_ak]

1984 is a good read... It will let you know there is always a cracking point for every one... And for some people it's a rat in a cage. It was also a good apple comercial

[SlippShodd]

I think I was eight or nine when I read 1984.
read lord of the flies and lord of the rings right about then too.

Me too.
And look how we turned out.
:)

mike