Sorry Nexa, this will be boring. Skip it. Maybe my next post will be about something really exciting, like the fluctuation-dissipation theorem.
MentalFrog wrote:
yossarian wrote:
paulsol the Flatulent wrote:
Quote:
For example, a triangle following the equator one quarter way around the Earth and having two right angles to the North, meet at the North Pole and form a third right angle, total sum of angles is 270 degrees!)
Ummm...I'm feeling a bit thick. try as i might, I cant picture what your sayin here...
edit. Im sure you're right tho.....
Edited, Apr 10th 2007 9:24pm by paulsol Take a globe. Put a dot at the north pole. Put two dots on the Equator - make them one quarter of the circumference apart. Connect the dots with the shortest possible lines (over the surface of the sphere). They are not straight lines in space, but appear straight locally on Earth.
Measure each interior angle of the triangle. They sum to more then 180 degrees. Here's why:
Each angle on the equator is from the equator to due North, and thus are right angles. Those two alone sum to 180 degrees (90+90).
The angle at the North pole is actually also 90, if you put the two dots exactly one quarter the way around the globe. This doesn't really matter for the argument - only that the sum of the angles on a curved surface don't sum to 180 - so I know it may be difficult to prove to yourself that the sum is actually 270 (that the angle at the North pole is 90).
A triangle is a polygon with three vertices and three sides
which are straight line segments.
You're not making straight lines. You're drawing a line along the curvature of the earth's surface. So it's not really a triangle is it?
That is acceptable. Let's call it a MentalTri, in that case.
1. The angles of a triangle sum to 180.
2. Schoolchildren everyday sum these angles and find 180 (just like we open jars of peanut butter every day and do not observe new life).
3. "Scientists" tell us that the Earth is curved, and that, in fact, the schoolchildren are drawing MentalTris, and the angles should add to more then 180.
4. Obviously the "scientists" are wrong and the Earth is flat.
5. This line of reasoning is wrong for analogous reasons to why the linked video is wrong.