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Category Archives: Geometri
Conical sections
The force of gravity determines the trajectories of the celestial bodies. Mathematical analysis reveals that there are three types of trajectories possible for a body moving in a gravitational field determined by Newton’s law of gravity. If one of the … Fortsätt läsa
Publicerat i Geometri, Gymnasiematematik(high school math), matematik 2c
Märkt Apollonius, conical sections, gravity, Newton
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Similarity
Two triangles are similar if all the corresponding angles are equal. Then the ratios of the corresponding sides to each other are the same for both triangles. In the fig above AB/BC = DE/EF or AB/DE = BC/EF. A list … Fortsätt läsa
Publicerat i Geometri, Gymnasiematematik(high school math), matematik 2c
Märkt fractals, Matematik 2c, Sierpinski triangle, similarity
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Cylindrical coordinates
Cylindrical coordinates can be considered as a hybrid between spherical coordinates and rectangular coordinates. The coordinates of a point is given by the angle between the projection of the point in the xy-plame Φ and two distances: the distance from the … Fortsätt läsa
Dimensions and different coordinate sytems
The number of figures necessary for specifying the position of a point is called the dimension of the space. For a two dimensional space it is sufficient to use two numbers (x, y) : one specifying the position on a … Fortsätt läsa
Publicerat i Algebra, Geometri, matematik 1c, Uncategorized
Märkt coordinatesystems, dimensions
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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 … Fortsätt läsa
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
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 = √ … Fortsätt läsa
Some geometric theorems: Menelao’s, Ceva’s, Simson’s line and Stewart’s
In Linneus backyard: Möckelsnäs manor house, Älmhult 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 … Fortsätt läsa
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 … Fortsätt läsa
Publicerat i Geometri, matematik 1c, Vectors
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