Two different great circles are only parallell at to places. The line of equator is of course straight line, bcause it is a great circle, but think of the latitude 80 degrees north circle, it's certainly not straight! If you don't believe me, suppose you stand 10 meters sout of the North Pole and go straight west 63 meters or so, is a straight line the first you will think of? Of course no. I haven't made a study of 3D spherical geometry though.I cannot think that all circles of a sphere parallell to eachother all the way round can be concidered straight on the surface. On a sphere, one might use a line which is slightly off the gr. ![]() ![]() The first line would cut across the top row and extend some distance outward, until it is in line with a point in each of the three dots in the middle row. My response was based on the basis that the problem was solved on an infinite square grid, rather than a sphere. The solution of Ivan is neat, and outside the box, but. (Like design the positions of the dots as a capital Z kind of shape.) If you let this property go, then we can draw any sloppy squares, and we can find a solution very easy. Is it important to use the word 'perfect square' and use the property '12 pairs of exactly the same distance in between'? Yes! What about putting them on a sphere? Can we put 9 dots in a 'square' on the surface of a square, so you can find 12 pairs with equal distance between them? Is it still a perfect square?Īnd if we find a perfect square with the properties above, is the solution of Ivan's problem still valid? In a flat plane there are the same distance between 1 and 2, as between 5 and 8, right? It's easy to see that there are 12 pairs that have the same distance between them. or do we mean "arranged in a *perfect* 3x3 square."? 'twas probably the first genuinely neat/beautiful solution I ever saw.ĭraw nine dots so that they are arranged in a 3x3 square. Good job on thinking outside the box! However, I came across this problem when I was in school, and there is a very neat solution which is also "outside the box". But the question was how to connect the spot wi have to keep in mind that the problem is translated in 3D.ĭoes that have any sense to you ?Curiously, you use the phrase "project your problem onto a sphere" - but the thing is, the reason your problem works is because there is no decent projection from a flat plane onto a sphere! (and everyone is busy thinking in flat space.)Īnyway, your solution is certainly correct, especially since we live on a sphere. I got the task from my teacher in high school. They are perfectly straight, you just have to keep in mind that the problem is translated in 3D. So three lines are : north pole-south pole, south pole-north pole and again north pole-south pole. ![]() And connect them with 3 straight lines (you change the directions of your pen on north and south pole). Look, it seems pretty natural to plant your 9 spots here. When I presented my anwser to my teacher in high school, he told me that's wrong and other students made fun of me □ So you pick 3 evenly distant meridianes and place your dots. sphere meridianes are perfectly straight if you look at them from the right angle. I had an idea of doing it with three straight lines (i projected my problem on a sphere). But the question was how to connect the spot with 4 lines. But what about three.ĭraw nine dots so that they are arranged in a 3x3 square.Ĭan you connect all nine dots with 3 STRAIGHT lines without taking pen (or pencil or chalk or other marking-tool) from paper? Ok, we know how to do it with 4 straight lines.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |