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The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up…
We humans haven't changed much since our remote ancestors roamed the African savannah. Our brains evolved to cope with the human-scale environment. So it is surely remarkable that we can make sense of phenomena that confound everyday intuition: in particular, the minuscule atoms we're made of, and the vast cosmos that…
The horizontal axis here is level of taxation, and the vertical axis represents the amount of revenue the government takes in from taxpayers. On the left edge of the graph, the tax rate is 0%; in that case, by definition, the government gets no tax revenue. On the right, the tax rate is 100%; whatever income you have…
Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is…
Phrases like “things are looking up” and “look at the upside” once meant something like “consider the good in the situation,” but they went through an ironic shift in the solar system’s early spacecolonial culture, mutating in the microgravity of early tin-can stations to mean a variety of practically sarcastic…
This meant, then, that the Greeks, in attempting to communicate their mathematical conceptioning, defined the circle as "an area bound by a closed line of equal radius from one point," the triangle as "an area bo)ound by a closed line of three angles, three edges, and three vertices." The Greeks talked only of the…
Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature…
The sun's rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the…