Category Archives: Gymnasiematematik(high school math)

Chord-tangent theorem

Publicerat den augusti 2, 2012 av mattelararen

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

Publicerat den augusti 2, 2012 av mattelararen

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

Heron’s formula

Publicerat den juli 29, 2012 av mattelararen

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 →

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

Number theory-more on numbers

Publicerat den maj 23, 2012 av mattelararen

De första talen människan använde sig av var förmodligen positiva heltalen de sk. naturliga talen. De användes för att ange kvantiteter av olika ting: fem tomater, 10 persikor etc.. Då människan började med handel kunde man bli skuld satt och … Fortsätt läsa →

Publicerat i Gymnasiematematik(high school math), matematik 1c | Märkt , | 5 kommentarer

Symmetries, translations and dilatations

Publicerat den april 16, 2012 av mattelararen

A good definition of symmetry was given by the mathematician Hermann Weyl:  An object is symmetrical  if, after you performed an operation on it, it still looks the same as it did before. A function can be moved in the … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), Uncategorized | Lämna en kommentar

Definite integrals

Publicerat den april 2, 2012 av mattelararen

In a geometrical context the integral can be interpreted as the area between the graph of the integrand f(x) and the x-axis. The idea is to summarize infinitely many infinitely thin rectangles. (An alternative approach to areacomputation is the Lebesgue-integration where you … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt | 1 kommentar

Indefinite integrals

Publicerat den mars 28, 2012 av mattelararen

If you need to calculate the distance travelled when you know the velocity as a function of time , since s'(t) = v(t) you need to be able to perform antiderivation i.e. finding a function whose derivative equals your function. … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt , | Lämna en kommentar

Differentiating the natural logarithm, products and quotients

Publicerat den mars 26, 2012 av mattelararen

In order to be able to deduce the derivative of the natural logarithm we resort to using implicit differentiation. Let x= ey(x) Differentiating both sides gives dx/dx = d ey(x)/dx 1=ey(x) dy(x)/dx Solving for dy(x)/dx one obtains dy(x)/dx = 1/ey(x) … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt , , | Lämna en kommentar

Pi-day

Publicerat den mars 16, 2012 av mattelararen

March the 14th. has officially been named the international π-day to honour this magical number which equals the ratio of the circmference to the diameter for all circles. http://www.wikihow.com/Celebrate-Pi-Day In 1882 the german mathematician Ferdinand Lindemann showed that pi is … Fortsätt läsa →

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

Differentiation of the trigonometric functions

Publicerat den mars 9, 2012 av mattelararen

To be able to differentiate the trigonometric functions one needs some standard limits: With the aid of these and the definition of the derivative it is possible to show that f(x)= sin (x) implies  f ‘(x) = cos(x) and f(x) … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 4 | Märkt | Lämna en kommentar