Inįact, the excess (for the special case shown, the extra $90$ degrees) is It turns out that for him the sum of theĪngles of the triangle is always greater than $180$ degrees. So there is noĭoubt that for him this triangle has three right angles, or Point, and also meets the first line with a right angle. Very special length he has chosen he gets right back to his starting Suppose our bug starts at the north pole and makes a straight line all He can, for example, find triangles which have three Our friend on the sphere can find triangles that are very Let’s take the case of a triangle on a plane. Is large the measurement can be done more crudely. Square is very small you will need a lot of accuracy, but if the square YouĬan find out that you live on a ball by laying out a square. To circumnavigate the globe in order to find out that it is a ball. Isn’t necessary to be able to lift yourself out of the plane in order toįind out that the world that you live in is curved. The geometry of the bugs on the sphere or on the hot plate is the Space to be a space in which the geometry is not what we expect for a Something was the matter with their space. That just by geometrical measurements they would discover that Larger scale they would discover that something was wrong. Then as they tried to make accurate squares on a That they had checked him out roughly by making crude measurements on a Now suppose that our bugs had each had their own Euclid who had told them what geometry “should” be like, and Mike The Feynman Lectures on Physics New Millennium Edition Your time and consideration are greatly appreciated. So, if you can, after enabling javascript, clearing the cache and disabling extensions, please open your browser's javascript console, load the page above, and if this generates any messages (particularly errors or warnings) on the console, then please make a copy (text or screenshot) of those messages and send them with the above-listed information to the email address given below.īy sending us information you will be helping not only yourself, but others who may be having similar problems accessing the online edition of The Feynman Lectures on Physics. This type of problem is rare, and there's a good chance it can be fixed if we have some clues about the cause. which operating system you are using (including version #).which browser you are using (including version #).If it does not open, or only shows you this message again, then please let us know: So, please try the following: make sure javascript is enabled, clear your browser cache (at least of files from ), turn off your browser extensions, and open this page: If you use an ad blocker it may be preventing our pages from downloading necessary resources. If you have have visited this website previously it's possible you may have a mixture of incompatible files (.js. In order to read the online edition of The Feynman Lectures on Physics, javascript must be supported by your browser and enabled.

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Straight line geometry of space time