# Månadsarkiv: augusti 2012

## Bessel functions

Friedrich Wilhelm Bessel (1784-1846)  was an outstanding mathematician and astronomer in the 19 th. century. Professor at the Albertina university in the no longer existing town of Königsberg. He was the first astronomer to use the parallax of a star … Läs mer

Publicerat i Calculus | | 2 kommentarer

## Line integrals

The line integral along the curve C can be written as where C is parametrisized as r(t) with the parmeter t. ∫¦r'(t)¦ dt equals the arc length i.e. the length of the curve. Consider eg the circle.  x2+ y2 = r2. … Läs mer

Publicerat i Gymnasiefysik(high school physics), matematik 5 | Lämna en kommentar

## Exercises on the masterclass

Publicerat i Uncategorized | 2 kommentarer

It is impossible to arrive at any destination since at first you have to travel half the distance and then half the remaining distance and so on. This eans you have to travel an infinite number of half-distances which ought … Läs mer

Publicerat i Gymnasiematematik(high school math), Uncategorized | Märkt , | 2 kommentarer

## Shooting stars

The perseids is a meteor shower connected to the comet Swift-Turtle. This picture shows this year’s Perseid shower photographed over Wirkenheim in Germany. http://en.wikipedia.org/wiki/Perseids

Publicerat i Astronomy | Lämna en kommentar

## Human achievement and technological triumph

Last Monday August 6 th. a human made automobile called ‘Curiosity ‘ landed on the surface of planet Mars. Even though it is our closest neighbour the journey lasted for 36 weeks.  It defied the ‘Mars curse’ and the landing was successful. It … Läs mer

Publicerat i Astronomy | Lämna en kommentar

## Masterclass in mathematics

Last week I supervised a masterclass in mathematics for 18 -years olds at Spyken Gymnasium in Lund. The subject was plane euclidean geometry. Above is a picture of the participants.  Which includes memebers of the Swedish IMO team Rdio interview: … Läs mer

Publicerat i Uncategorized | Märkt | Lämna en kommentar

## Chord-tangent theorem

The measure of the angle formed in the intersection between the chord of a circle and the tangent to the circle is the same as the angle at the periphery of the circle. Click here to se the proof

## Euclidean postulates, theorems and definitions 3

Geometri teorem den 29 juli 2012 00:02 Om två vinklar är vertikalvinklar är de båda vinklarna lika stora. (If two angles are vertical angles then the two angles are congruent.) Två trianglar är kongruenta (likadana) om två sidor och mellanliggande … Läs mer

Publicerat i Geometri, Gymnasiematematik(high school math) | Märkt , | Lämna en kommentar

## Euclidean postulates, theorems and definitions 2

1. The sum of the measures of the four interior angles of a convex quadrilateral is 360 degrees, a constant. Two triangles are congruent (i.e. identical) if two angles and a non- included side of the first triangle are congruent … Läs mer

Publicerat i Geometri | Märkt | Lämna en kommentar