[Guest]

Is it possible to create a triangle that has two right angles? If this puzzle is too simple for you, try this. What is the smaller angle between the minute hand and the hour hand when it is 5:12 on the dot?

If I draw a triangle from the North Pole/South Pole of a sphere to the equator.

84* If I am wrong, please explain.

[Guest]

The triangle has 2 sides of infinite length. The clock angle is 84degrees. The 12 minute hand has rotated 72deg from the top, and the hour hand has rotated just past the "5" by 1/5th hour, or what would be the 26 minute position, which is 156 deg rotation from the top. 156 - 72 = 84

[Guest]

I do not understand your spoiler for the triangle puzzle. As I see it a triangle by definition requires three angles, no more, no less, and to connect the two parallel lines that would be created by using two right angles would require no less than two more angles putting the shape over the three angle limit.

I do believe you are correct about the time problem though.

[Guest]

Okay ZAnDER, imagine a 3-dimensional sphere. Now, take the "North Pole". Draw two line segments straight across to the equator over the surface of the sphere. In theory, those two angles on the equator are right angles or 90 degrees. Also, on a circle (2-dimensional), if I draw two lines ANYWHERE from the diameter to the same point on the circumference, it's always a right triangle. So, when we blow up the circle into a sphere, the lines become curved on the flat surface of the sphere. If you do not understand, look at any ball. Now, look at the middle or the equator of the Earth. Now, do you see how it has straight lines that are parallel JUST before the equator? Well, if we measure the the angles there, we get two right angles. This is my explanation for that problem. It is a little confusing but if you look at it just the right way, you'll find the solution.

[Guest]

TeaseMe... you are correct according to my calculations on the clock puzzle. On the triangle one though, you should see my response to ZAnDER because I did that puzzle differently. I also did the clock puzzle differently. I did that for every interval from in each hour is equal to 12 minutes. Each interval is also equal to 6 degrees. Then, each interval is also 2 minutes of time. So count the intervals then multiply that number by 6. Then, you get 84 degrees.

[Guest]

Okay ZAnDER, imagine a 3-dimensional sphere. Now, take the "North Pole". Draw two line segments straight across to the equator over the surface of the sphere. In theory, those two angles on the equator are right angles or 90 degrees. Also, on a circle (2-dimensional), if I draw two lines ANYWHERE from the diameter to the same point on the circumference, it's always a right triangle. So, when we blow up the circle into a sphere, the lines become curved on the flat surface of the sphere. If you do not understand, look at any ball. Now, look at the middle or the equator of the Earth. Now, do you see how it has straight lines that are parallel JUST before the equator? Well, if we measure the the angles there, we get two right angles. This is my explanation for that problem. It is a little confusing but if you look at it just the right way, you'll find the solution.

You are correct except for one minor thing you are replacing line segmants with curves.

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments... In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points... The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth.

[Guest]

There seems to be confusion because the two geometries; one for flat surfaces, plain geometry; another for spheres, spherical geometry, have different sets of definitions for the same terms. Plain geometry defines a straight line as connecting two points in the shortest distance. in spherical geometry the shortest distance between two points is a curved line. It is this difference that airlines use to get from one airport to another distant airport in the shortest time and with the least fuel use. Also, this is the reason a flat surface cannot represent the surface of a sphere. A map of the earth that has a longitudinal and latitudinal grid with all intersections at right angles seriously distorts the area of all countries at any distance from the equator.

In plain geometry a triangle is defined to have 180 degrees as the sum of all three angles. This is not so in spherical geometry. Therefore, one cannot compare triangles from the two disparate geometries.

[Guest]

Okay, this was a riddle that was sort of different the way I looked at it. jimtallcott does say that my thoughts are correct but he says I cannot compare triangles from two different dimensions. In the beginning when I said "triangle", I meant a triangle from anywhere. Instead of being on a plane, it's on a 3-dimensional SURFACE. Maybe I was a little off track but I apologize for that. Also, welcome to BrainDen jimtallcott!

[Guest]

Many individuals who think of triangles limit themselves to Euclidian geometry, also known as plane geometry, yet there are non-Euclidean geometries. One of the non-Euclidean geometries is spherical geometry, the simplest form of elliptic geometry, where a line has no parallels through a given point, and another is hyperbolic geometry, where a line has two parallels and an infinite number of ultraparallels through a given point. As the question asks if (it is possible if) a triangle (a polygon of three angles) can have two right angles (two angles of 90 degrees each), we can answer "yes". The sum of the angles of a spherical triangle is between 180 degrees and 540 degrees, thus, if the sum of the angles is greater than 180 degrees, two of the angles can be right angles with the third angle equal to the remaining difference.

A clock is divided into 60 equidistant minute marks. The hour hand moves to a new minute mark every 12 minutes. Thus, at 5:12, the hour hand is one minute mark past the 5 while the minute hand is on the 12 minute mark. As each minute is 1/60 of the circle, i.e., 6 degrees, and each hour is 1/12 of the circle, i.e., 30 degrees, the angle is the difference of 5x30 degrees + 6 degrees and 12x6 degrees, i.e., 84 degrees.

[Guest]

Taking your globe example.

The arks connecting the points, called geodesics, may be able to replace lines in spherical geometry but then a new name is given to each of the shapes resulting from that adjustment of definition. They are all prefixed with spherical -. So your Triangle would not be called a triangle because it is not one, it would be called a spherical triangle.

[Guest]

Okay ZAnDER, imagine a 3-dimensional sphere. Now, take the "North Pole". Draw two line segments straight across to the equator over the surface of the sphere. In theory, those two angles on the equator are right angles or 90 degrees. Also, on a circle (2-dimensional), if I draw two lines ANYWHERE from the diameter to the same point on the circumference, it's always a right triangle. So, when we blow up the circle into a sphere, the lines become curved on the flat surface of the sphere. If you do not understand, look at any ball. Now, look at the middle or the equator of the Earth. Now, do you see how it has straight lines that are parallel JUST before the equator? Well, if we measure the the angles there, we get two right angles. This is my explanation for that problem. It is a little confusing but if you look at it just the right way, you'll find the solution.

It is non-Euclidean geometry. I'd consider this quiz as an introduction to this math topic rather than a brain teaser. We don't use set of math knowledge in our daily life, so it seems to be unfair for those who has never heard of it(disregarding longitude and latitude on the globe).

[Guest]

It is non-Euclidean geometry. I'd consider this quiz as an introduction to this math topic rather than a brain teaser. We don't use set of math knowledge in our daily life, so it seems to be unfair for those who has never heard of it(disregarding longitude and latitude on the globe).

No it is a valid question because ignorance is not an excuse for anything. It is just an incorrect answer

[Guest]

I never said wether it was in 2-dimensional surface or 3-dimensional surface. Also, Ordinary Level, I really like math and have been 2nd place in a math competition in NJ and NYC and 19th in USA.

[bonanova]

Not so much a puzzle in logic as in geometry.

It has been discussed in response to

[Guest]

Okay, I'm sorry bonanova about that mistake. Also, how do you copy what people say in the green rectangle thing? Can you tell me?