Draw a circle and divide the circumference into and even number of equally spaced points. In this example I have used 44: Draw following chords between numbers in such a way that when viewed as a sequemce, the second point of each pair moves twice as fast around the circle.: and and on completion, sketch …
t-Formulae are used in integration to tackle rational expressions of tigonometric functions. After a spell in the cold, when they were not included in some A level specifications, they are now back in sixth form lessons. It all starts with the subsitution, from which the following functions can be derived, , , . These derivations …
Once has been defined as the ratio circumference to diameter, the area of a circle must be . A proof relies on an infinite, limiting process which paves the way to some calculus-like ideas. A circle is cut up into 6 sectors which are then rearranged into a near rectangle, What doesn’t look too close …
There’s always space on the inter-web for another proof of Pythagoras’s Theorem. Here’s one that uses the following equal areas property of parallelograms. This kind of area chopping and shape translation is a feature of Euclidean geometry and our senses support it’s veracity at the order of size of the classroom. The squares on the …
Parallelograms generalise Pythagoras to any triangle Read More »
Conic sections in the sand give shipwrecked Socratic philosopher, Aristippus, good hope. I wonder if this ancient tale, in which the mathematics of planetary motion some 2000 years prior to it’s application in space travel, is used to signify the presence of intelligent life and therefore hope of salvation has some echo in our …
Conic sections in the sand give shipwrecked philosophers good hope Read More »
First definition of triangles from Euclid’s Elements Book I (Fundamentals of Plane Geometry Involving Straight Lines), Definition 20.
Ancient theorem of Euclid (Book III, Proposition 31) still a fundamental part of school maths. The angle in a semi-circle is a right angle.
Rotations in space make good Saturday morning maths at the King’s School.
In the geometry of mariners, where straight lines are Great Circles, the angle sum of a triangle is more than 180 degrees.
