[sparkyboy6]

Well, can you?

[bonanova]

  On 11/6/2010 at 8:25 PM, sparkyboy6 said:

Well, can you?

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If by regular triangle you mean equal sides and angles but not necessarily straight sides.

Draw arcs of great circles among these three points:

.

1. North Pole
2. Equator at 0^o longitude
3. Equator at 90^o longitude
   .
   

[Guest]

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or if the sphere was big enough, say the size of earth, then arcs would be negligible and you could just draw one at your feet and no one would be able to tell the difference

[Guest]

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Since a regular triangle is a plane figure, it cannot be drawn on a sphere.

[Guest]

  On 11/6/2010 at 8:25 PM, sparkyboy6 said:

Well, can you?

Yes, but the sphere would have to be infinitely large.

[peace*out]

  On 11/6/2010 at 9:52 PM, bonanova said:

  Reveal hidden contents

If by regular triangle you mean equal sides and angles but not necessarily straight sides.

Draw arcs of great circles among these three points:

.

1. North Pole
2. Equator at 0^o longitude
3. Equator at 90^o longitude
   .
   

Say we said that the triangle had to be 2-D

We couldn't unless the sphere was crazy large and one point on it could somehow fit three points, which connected to create a triangle...

I'd agree with Dragoon on this one if the triangle is 2-D, and BN if the triangle could have depth...

[Guest]

Wonder if you could kindly clarify what you mean by "regular triangle".

[Guest]

  On 11/6/2010 at 9:52 PM, bonanova said:

  Reveal hidden contents

If by regular triangle you mean equal sides and angles but not necessarily straight sides.

Draw arcs of great circles among these three points:

.

1. North Pole
2. Equator at 0^o longitude
3. Equator at 90^o longitude
   .
   

One would assume that "regular" implied interior angles totaling 180 degrees.

[Guest]

  On 11/7/2010 at 2:42 AM, peace*out said:

Say we said that the triangle had to be 2-D

We couldn't unless the sphere was crazy large and one point on it could somehow fit three points, which connected to create a triangle...

I'd agree with Dragoon on this one if the triangle is 2-D, and BN if the triangle could have depth...

Thanks for your support, but please amplify on "could have depth"

[peace*out]

  On 11/7/2010 at 3:53 AM, Dragoon said:

Thanks for your support, but please amplify on "could have depth"

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**Please tell me if im wrong - this is jsut my thinking...

what i meant originally was that it the triangle was on a sphere, the corners and lines would be at different points. (i dont have paint on this comp, so i cant really explain it visually but...) the sphere as a 3D object has depth. it is 3D - Length, height and depth. A sphere is made up of many different points (thanks Intro to D&D) and the general idea of a sphere is a 3D circle. If the edge of a circle is like a parenthisee --> ( , then not all parts of the triangle would be at the same point lining up...the lines would be curved. Does that make any sence?

Rethinking it, i think that the answer is "No."

A sphere is made up of many points. You could have three points be in the same plane but not the lines. A triangle is a polygon. The meaning of polygon is "many sided." (I know that this is not the exact definition, but the criteria fits -->) A polygon is a shape without any curves or open sides or crossing likes. Ex: this is not a polygon: D U O L M N H Z. The triangle in side A is, but not the "A" itself, because the sides are open...

A sphere is made up of many points.

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sphere, in geometry, the three-dimensional analogue of a circle. The term is applied to the spherical surface, every point of which is the same distance (the radius) from a certain fixed point (the center), and also to the volume enclosed by such a surface. The curve formed by a plane cutting a sphere is a circle. If the plane goes through the center of the sphere, the circle is called a great circle of the sphere. It is the largest circle that can be drawn upon the sphere, and all great circles of the same or equal spheres are of equal size. The shortest distance between two points on a spherical surface, measured on the surface, is the distance along the great circle through those points. A plane cutting a sphere in a great circle divides the sphere into two equal segments called hemispheres. The diameter of a sphere is the diameter of one of its great circles. The formula for the area of the surface of a sphere is S=4πr2, and for the volume it is V= 4-3 πr3, where r is the radius of the sphere. Spherical geometry and spherical trigonometry are methods of determining magnitudes and figures on a spherical surface.

The Columbia Electronic Encyclopedia® Copyright © 2007, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

sphere

In geometry, the set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters. The components and properties of a sphere are analogous to those of a circle. A diameter is any line segment connecting two points of a sphere and passing through its centre. The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre. A meridian is any great circle passing through a point designated a pole. A geodesic, the shortest distance between any two points on a sphere, is an arc of the great circle through the two points. The formula for determining a sphere's surface area is 4πr2; its volume is determined by (⁴⁄₃)πr3. The study of spheres is basic to terrestrial geography and is one of the principal areas of Euclidean geometry and elliptic geometry.

For more information on sphere, visit Britannica.com. Britannica Concise Encyclopedia. Copyright © 1994-2008 Encyclopædia Britannica, Inc.

sphere

1. Maths

a. a three-dimensional closed surface such that every point on the surface is equidistant from a given point, the centre

b. the solid figure bounded by this surface or the space enclosed by it. Equation: (x--a)2 + (y--b)2 + (z--c)2 = r2, where r is the radius and (a, b, c) are the coordinates of the centre; surface area: 4πr2; volume: 4πr3/3

2. the night sky considered as a vaulted roof; firmament

3. any heavenly object such as a planet, natural satellite, or star

4. (in the Ptolemaic or Copernican systems of astronomy) one of a series of revolving hollow globes, arranged concentrically, on whose transparent surfaces the sun (or in the Copernican system the earth), the moon, the planets, and fixed stars were thought to be set, revolving around the earth (or in the Copernican system the sun)

^^ There's three definitions to work with, and unless i missunderstood, the surface of a sphere is curved. Which means the lines of a the triangle cant be strait.

[bonanova]

  On 11/7/2010 at 3:38 AM, Dragoon said:

One would assume that "regular" implied interior angles totaling 180 degrees.

In geometry, "regular" has a particular meaning with regard to polygons: equal length sides and angles.

With that meaning, for example, regular rectangle refers to a square.

.

1. There is a geometry of the plane, denoted as plane geometry or Euclidean geometry.
   The interior angles of all Plane triangles, regular or not, sum to 180^o.
   .
   
2. There is a geometry of the sphere denoted as spherical geometry.
   The interior angles of Spherical triangles sum to a value between 180^o and 540^o.
   .
   
3. There is also a hyperbolic geometry.
   The interior angles of Hyperbolic triangle sum to a positive value less than 180^o.
   .
   

The OP did not specify that the triangle was be a plane triangle, nor could it, sensibly.

As peace*out notes, on the surface of a sphere no plane figure can be drawn.

[sparkyboy6]

  On 11/7/2010 at 10:19 AM, bonanova said:

In geometry, "regular" has a particular meaning with regard to polygons: equal length sides and angles.

With that meaning, for example, regular rectangle refers to a square.

.

1. There is a geometry of the plane, denoted as plane geometry or Euclidean geometry.
   The interior angles of all Plane triangles, regular or not, sum to 180^o.
   .
   
2. There is a geometry of the sphere denoted as spherical geometry.
   The interior angles of Spherical triangles sum to a value between 180^o and 540^o.
   .
   
3. There is also a hyperbolic geometry.
   The interior angles of Hyperbolic triangle sum to a positive value less than 180^o.
   .
   

The OP did not specify that the triangle was be a plane triangle, nor could it, sensibly.

As peace*out notes, on the surface of a sphere no plane figure can be drawn.

Right, can you draw a 180* triangle on a sphere the size of a tennis ball?

[pdqkemp]

  On 11/7/2010 at 11:06 AM, sparkyboy6 said:

Right, can you draw a 180* triangle on a sphere the size of a tennis ball?

Bonanova said the triangle on a sphere would be between 180 and 540 degrees. I THINK this means that the larger the sphere, the closer the triangle's angles would add up to 180 degrees; the smaller the sphere, the closer the triangle's angles would add up to 540 degrees.

[sparkyboy6]

  On 11/7/2010 at 12:03 PM, pdqkemp said:

Bonanova said the triangle on a sphere would be between 180 and 540 degrees. I THINK this means that the larger the sphere, the closer the triangle's angles would add up to 180 degrees; the smaller the sphere, the closer the triangle's angles would add up to 540 degrees.

Ok, here's the question simplified. Would it be a triangle?

[pdqkemp]

  On 11/7/2010 at 1:06 PM, sparkyboy6 said:

Ok, here's the question simplified. Would it be a triangle?

Again - going completely by what Bonanova said, "YES". This would be a Spherical Triangle as defined in Spherical Geometry. In Spherical Geometry, a Spherical Triangle is a "normal" triangle.

If you posted this must follow the definitions in Euclidean Geometry, then of course the answer is "no".

See Bonanova's post for the links.

[sparkyboy6]

Bonanova got it right!

[bonanova]

  On 11/7/2010 at 12:03 PM, pdqkemp said:

Bonanova said the triangle on a sphere would be between 180 and 540 degrees. I THINK this means that the larger the sphere, the closer the triangle's angles would add up to 180 degrees; the smaller the sphere, the closer the triangle's angles would add up to 540 degrees.

The relative size of the triangle and sphere determines the angles.

More precisely, the solid angle subtended by the triangle is what matters.

On a sphere the size of the earth or the size of a marble, either one,

a triangle with vertices all on a great circle has a 540^o sum,

for both the internal and external angles.

[pdqkemp]

  On 11/7/2010 at 9:31 PM, bonanova said:

The relative size of the triangle and sphere determines the angles.

More precisely, the solid angle subtended by the triangle is what matters.

On a sphere the size of the earth or the size of a marble, either one,

a triangle with vertices all on a great circle has a 540^o sum,

for both the internal and external angles.

Ah....I'm fairly sure my wee brain gets it now!

Thanks much for the further explaination, Bonanova!

[OmegaScales]

Theoretically, yes.

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On a perfectly spherical planet, take out some paper and writing tool, and draw the triangle. As gravity is specific to points, however, there are probably no perfectly spherical planets, only elliptoid ones. Using this logic, the actual answer is no. Nowhere did you say that I had to draw it onto the sphere.

[Guest]

I agree, in general, with the comments of peace*out and Bonanova, but I think you are still dealing with finite sheres. Once you expand the sphere to the infinite a regular triangle inscribed on the surface is bound to be regular. And peace*out, at the infinite would not the depth cease to exist?

[peace*out]

  On 11/8/2010 at 6:26 AM, Dragoon said:

I agree, in general, with the comments of peace*out and Bonanova, but I think you are still dealing with finite sheres. Once you expand the sphere to the infinite a regular triangle inscribed on the surface is bound to be regular. And peace*out, at the infinite would not the depth cease to exist?

true...

And to bonanova: me and my limited 9th grade mind hasn't learned yet that there are other kinds of triangles...Thank goodness I have geometry today