Triangles on Earth Exceed 180 Degrees

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 to 180 degrees. However, in the last century people began to realise that other forms of geometry were possible in which the angles of a triangle need not add up to i8o degrees...

 Math Problem: How Long Until the Earth Falls Into the Sun?

Our earth has orbital motion, revolving once around the sun in about 365 days. Suppose that this orbital motion suddenly stopped completely, but everything else remained the same. How long would it take for the earth to plunge along a straight line into the sun? [...] Kepler's law applies to planetary orbits, whether they be of circular, or elliptical shape. It says that T22/T12 = R23/R13, where T is the period of an orbit and R is its semi-major axis. The semi-major axis is the average of th...

 Human Respiration is Carbon Neutral

The very first time you learned about carbon dioxide was probably in grade school: We breathe in oxygen and breathe out carbon dioxide. Any eight-year-old can rattle off this fact. More specifically, the mitochondria within our cells perform cellular respiration: they burn carbohydrates (in the example shown below, glucose) in the oxygen that we breathe in to yield carbon dioxide and water, which we exhale as waste products, as well as energy, which is required to maintain...

 The Laffer Curve

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, whether from a business you run or a salary you’re paid, goes straight into Uncle Sam’s bag. Which is empty. Because if the government vacuums up every cent of the wage you’re ...

 Geometry Seems Disconnected from Reality

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 exhibits not simply a higher degree but an altogether different level of complexity.