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 … Fortsätt läsa

Publicerat i Calculus | Märkt , | 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. … Fortsätt läsa

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

Exercises on the masterclass

Publicerat i Uncategorized | 2 kommentarer

Zeno’s paradoxes

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 … Fortsätt läsa

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 … Fortsätt läsa

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: … Fortsätt läsa

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

Publicerat i Geometri, Gymnasiematematik(high school math), matematik 1c, Uncategorized | Märkt , | Lämna en kommentar

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 … Fortsätt läsa

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 … Fortsätt läsa

Publicerat i Geometri | Märkt | Lämna en kommentar