Given a solid sphere, construct its diameter using compass and straightedge.

I've thought for about 20 seconds, but i will keep the answer, because revealing it will decrease others' fun

CLUE 1: the use of the compass is to 'LOCK' the direction, or the point

need more clue? let me know.

1) Generate an arbitrary disc inside sphere's volume, by taking any three points on sphere, making a triangle and then making perpendicular bisectors to each side to locate centre of the disc.

2) Generate another disc ensuring that it is not parellel to the first one.

3) Make a line perpendicular to plane of discs and passing thru their center (you can do this with a compass and ruler)

4) Point of intersection of lines thru 2 discs is centre of sphere.

5) Now diameteres may be drawn trivially.

take the pencil off the compass, scribble the graphite into a heavy line and then roll the ball along the length of the straight edge.

you`ll get 2 pencil marks the distance between them will be the circumference, the maths is easy from there

 

[edit] I just realised in this post, that it requires a measuring device (a rule) so ignore me!

wait till the sun is directly above you. (you may have to move to a different place on earth) . lay the sphere on the piece of paper. and trace the circle from its shadow

go with pulkit. bloodhound is retarded, so ALWAYS ignore him.

What do you mean? bloodhound's made perfect sense. Though he didn't describe how to draw the diameter, it's pretty simple once you have a circle.

I think its more of a mathematical problem. You don't acctualy have a real life sphere to work with !

It is a construction. That means you use a compass and straight edge. Pulkit was correct.

ok then. use the writing bit of the compass to trace the required circle then!!!. get the straight edge. measure the diameter. mark it with something. and then get a ruler and find out how long it is.

how do you suppose you measure the diameter then?

Who said you had to do that? And besides, bloodhound himself said you use a ruler.

the first post said that. "Given a solid sphere, construct its diameter using compass and straightedge."

 

a secant isn't nessecarily a diameter. how using a ruler? duh, just go with pulkit. it is an easy construction.

pulkit's actualy seems rather complex in comparison to bloodhound's. Also, finding the widest part of the circle would be the diameter. If you're impying that you can't find the diameter with guess and check, which I think you are, I would point out that using a compass has already negated any completely accurate answer.

if you have ever done a construction, you would know pulkit's way is easy and correct. bloodhound's way isn't even a construction. he wants to trace a shadow and make an arbitrary line to call the diameter.

Personaly, I found constructions to be just about the most useless thing I've ever waisted time on in math class. I don't see how pulkit's way is at all easy. One problem I see is drawing inside a sphere with a compass. That could be difficult. But then again you were probably only going for theoretical answers. And where is the flaw in bloodhound's answer. The shadow would be the circumfrence of the circle, right? And then finding the widest point would be the diameter. And thus it meets all the origional critirea.

the widest point would be hard to find. THAT ISN'T A CONSTRUCTION. all it is is tracing a shadow(which isn't neccessarily the correct size) and making a random secant.

But aren't we going for theoretical?

Also, finding the widest part of the circle would be the diameter

Given a circle, there is no one step way to find the diameter. You can't just pick up a ruler and measure the diameter, thats not a construction, neither is it a mathematically correct or accurate method. The widest part of the circle is not sitting there for you to come and find it.

I would point out that using a compass has already negated any completely accurate answer.

That is completely incorrect

But aren't we going for theoretical?

Theoretical yes. That is why you need a formal answer to the question.

That is completely incorrect

How so?

You must realize that this is a theoretical question. The compass is basically referring to the ability to draw loci at constt distances from a fixed point, it is not a physical instrument that has flaws in it. In fact there is this whole range of mathematical proofs on things you can do using a ruler and compass (over a hundred of these are attributed to a gentleman called Gauss).

And even if you use a real compass for any applications, it would also give you answers to a level of accuracy greater than you can get with most other methods.(Any inaccuracy would only be due to the physical/mechanical construction of the instrument and faults in that)

can't believe u guys are so serious. only trying to be creative!! had a look to find a proper solution. couldnt find one. anyway its just like that joke about finding a height of a building using a barometer.

anyway its just like that joke about finding a height of a building using a barometer.

Very true )

pulkit has it perfect

blood hound you are way off he wants you to draw a line through the center of the sphere that is all

Giving the mesure of a possible diameter is useless

can't believe u guys are so serious. only trying to be creative!! had a look to find a proper solution. couldnt find one. anyway its just like that joke about finding a height of a building using a barometer.

I wasn't entirely serious. I knew what they were saying, but I still don't like it. I guess that's why my math teachers never much cared for me. I always would find the simple way to these and be done. It seems too pointless to find a solution that is perfect "in theory" when "in theory" my solution would work just as well. Oh well, it's been a long time since I fought over constructions. It was fun.