Månadsarkiv: juli 2012

Heron’s formula

Heron who invented rhe first steam device also came up with a geometry formula. The circumference p of a triangle is related to the sides of of the triangle a,b and c and the trianglearea T through T = √ … Läs mer

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

Some geometric theorems: Menelao’s, Ceva’s, Simson’s line and Stewart’s

The Italian mathematician Giovanni Ceva’s published in 1678 Menalao’s theorem and that which is credited to him. Use Menlao’s theorem for collinearity and Ceva’s theorem för concurrency. Menelao’s theorem (named after MEnelaos from Alexandria  100 A.D) states that if points … Läs mer

Publicerat i Geometri | Märkt | Lämna en kommentar

Kurrebo, Urshult, An Eden in Sweden

Kurrebo, Urshult, An Eden in Sweden

The public garden and apple orchard in Urshult Sweden.
The northernmost applefarm in the world.With a fantastic roarium.

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Definition of groups

A group in mathematics has the following properties: There exist a set of elements p, q, r, …  and a binary operation which applied to p, q gives pq. The set is closed under this single-valued operation.  The associative law: … Läs mer

Publicerat i Algebra | Lämna en kommentar

Normalized coordinates

If A, b, c are three non-linear points, any vector P inside the triangle ABC may be expressed in terms of vectors A, B C thus: P =xA + yB + zC   with x + y + z = 0 and … Läs mer

Publicerat i Uncategorized | Lämna en kommentar

Collinearity

Theorem: If A, B and C are collinear points, then the real numbers x, y, z not all zero can be found such that x + y + z = 0 xA + yB + zC = 0. and also … Läs mer

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

More vector algebra

A clever way to express the equation of a line is to use the parameter form. If C is any point on the line determined by two points a and B then we may always write C = (1-t) A … Läs mer

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

Venus transit in H- alpha

Picture of Venus transit photographed with an Hα- filter. λ = 6566 A. Resolution 1 A. In this picture it is possible to cpmåare the size of the Earth to that of the Sun since Venus is of the same … Läs mer

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Linear dependence

The vectors P1, P2, P3, … are said to be linearly dependent if the real numbers k1, k2, k3, .. not all zero can be found so that k1P1 + k2P2 + ….. + knPn = 0. Since it is … Läs mer

Publicerat i Geometri, matematik 1c, Vectors | Lämna en kommentar