Category Archives: Uncategorized

Normalized coordinates

Publicerat den juli 14, 2012 av mattelararen

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 … Fortsätt läsa →

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Collinearity

Publicerat den juli 10, 2012 av mattelararen

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 … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

More vector algebra

Publicerat den juli 7, 2012 av mattelararen

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 … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

Venus transit in H- alpha

Publicerat den juli 6, 2012 av mattelararen

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 … Fortsätt läsa →

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Euclidean Definitions

Publicerat den juni 21, 2012 av mattelararen

A line has length between two points but no width. A point has no components i.e. it can’t be divided into parts. A straight line traces the closest distance between two points. A curved line has no straight segments. A surface … Fortsätt läsa →

Publicerat i Geometri, Uncategorized | 4 kommentarer

More Elements

Publicerat den juni 20, 2012 av mattelararen

There are two types of proof: Direct proofs: Where it is proved (deduced or induced) from the basic axioms, definiyions or earlier proved theorems that the statement is correct. Indirect proofs: The principle for this type of proofs is that … Fortsätt läsa →

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Euclidean Geometry

Publicerat den maj 29, 2012 av mattelararen

I have started to read Euclid’s ‘Elements’. This is perhaps the most influential book in mathematics and was used for more than two-thousand years in schools all over the western world. My edition is written by Christian Fredrik Lindman lecturer of … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

More vectorcalculus: Gauss theorem and Stokes theorem

Publicerat den maj 25, 2012 av mattelararen

Since the divergence of a vectorfield provides us with the number of field lines radiating outward from the source of the vectorfield it can be intuitively understood that the volume integral of the divergenbde of F equals the surface integral … Fortsätt läsa →

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The decimalsystem and some terminology

Publicerat den maj 17, 2012 av mattelararen

At this point it  might be wise to take a closer look at the decimalsystem which is the way we use to represent quatities in mathematics. The decimalsystem is a positionsystem (based on powers of ten)  which means that the value of … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

Divergence and curl of vectorfields

Publicerat den maj 11, 2012 av mattelararen

According to the Helmholtz-theorem a vectorfield is completely defined by the divergence and  curl of the vectorfield. the divergence is a measure of the strength of the source of the vectorfield whereas the degree of rotation of the field is given … Fortsätt läsa →

Publicerat i Calculus, Uncategorized, Vectors | 1 kommentar