## Tuesday, 24 June 2014

### Some Facts about Geometry – Math is Fun

If you are a fan of mathematics and enjoy reading some history whereas learning wherever several of our modern concepts came from then you will enjoy this article for sure. Realize fascinating facts and data associated with works made by the traditional Egyptians, Babylonians, Greeks and other well-known mathematicians.

So here are some facts about geometry which makes mathematics more fun:
• The word ‘geometry’ comes from the Greek words ‘geo’, which means earth, and ‘metria’, which means measure.
• Ancient Egyptians used geometric mathematics principles as way back as 3000 before Christ.
• Along with arithmetic, geometry was one amongst the 2 fields of pre-modern mathematics.
• Babylonians measured the circumference of a circle as just about three times the diameter that is fairly near today’s measuring that uses the worth of Pi (Near 3.14).
• Greek thinker and scientist philosopher Pythagoras lived round the year five hundred before Christ and is thought for his mathematician theorem concerning the 3 sides of a right angle triangle: a² + b² = c²
• The compass and straight edge were powerful tools within the advancement of geometry, permitting the development of assorted lengths, angles and geometric shapes.
• Archimedes of Syracuse lived round the year 250 before Christ and contends an outsized role within the history of geometry together with a technique for determinant the volume of objects with irregular shapes.
• Modern day geometry has created developments in an exceedingly range of areas, together with those who create use of the raw computing power of today’s computers.
Some facts about different shapes:
• Triangles are polygons with the smallest amount of sides (three).
• Whole concept of trigonometry is that the study of the link between the angles of triangles and their sides.
• All points on the surface of a sphere are at the same distance from the middle.
• Square shapes are typically utilized by humans for style and engineering functions like planning.
• The word ‘quadrilateral’ comes from ‘quad’ which means ‘4’ and ‘lateral’ which means ‘of sides’.
• A cube has the largest volume of all cuboids with a certain surface area.
• You can make 11 different ‘nets’ by folding out the 6 square faces of a cube.
Hope you have enjoyed reading this fun list. If you have something more to say please write in the comment section below.

## Thursday, 7 February 2013

### Development of Calculus

During the century before Newton and Leibniz the works of Greek mathematicians were popular, especially the work of Archimedes. Infinitesimal techniques were developed for calculating areas and volumes, and Johannes Kepler (1571-1630), shown at left, contributed to these developments.

His interest in calculating areas and volumes stemmed from an incident that occurred when he married for the second time in Linz, Austria, in 1613. Kepler had purchased a barrel of wine for the wedding and the wine merchant’s method of measuring the volume at first angered him. This inspired Kepler to study how to calculate areas and volumes and to write a book about the subject, Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), which was his main contribution to the development of the integral calculus.

The wine barrel incident also led Kepler to take up a problem of differential calculus, the problem of maximums: What is the best design for a barrel in order to maximize its volume? Today, we solve this problem using derivatives because we know that, at a maximum (or minimum) value of a differentiable function, the derivative of the function is zero.

Fermat was the first to relate maximum and minimum problems to tangents to curves: at a maximum or a minimum the slope of the tangent to the curve is zero. Kepler was able to show that, despite minor differences, the proportions of the Austrian wine merchant's barrels were such that the procedure used to calculate the volume actually would be quite accurate, after all.

## Friday, 17 August 2012

### Tangent

In geometry, the tangent line (or simply the tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point—that is, coincides with the curve at that point and, near that point, is closer to the curve that any other line passing through that point. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f'(c) where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.
The word tangent comes from the Latin tangere, to touch.

## Tuesday, 12 July 2011

### Convergence

Mathematics

Convergence (mathematics), refers to the notion that some functions and sequences approach a limit under certain conditions

Convergence (logic), the notion that a sequence of transformations come to the same conclusion, no matter what order they are performed in.