"Math-Assist" means Mathematical Assistant and that's exactly what this program is designed to be.It's for secondary level or high school students and teachers and anybody else who has anything to do with mathematics.

**Math-Assist helps in solving most of the tasks of :**

» Algebra

Prime numbers

The prime numbers or twin primes between two natural numbers a and b are calculated.

Prime Factorization

The prime fatorization of a natural number n < 1014 is calculated.

G.C.F. and L.C.M.

The greatest common factor (GCD) the least commun multiple (LCM) and the sets of divisors of up to 10 numbers are calculated.

Decimals to Fractions

Periodical decimals will be transformed to fractions.

Fractions to Decimals

Fractions are transformed in periodical decimals and also the period and its length are determined.

Binomials of n-th Degree

The binomial ( a·x + b·y )n with 1 < n < 500 is calculated.

Equations of 4-th Degree

The solutions of a·x4 + b·x3 + c·x2 + d·x + e = 0 is calculated .

Diophantine Equations

The integer solutions of a·x + b·y + c = 0 with a, b, c integer are calculated.

Pythagorean Triples

The pythagorean triples between two bounds are calculated.

Calculators

Calculation in place value systems

Calculation with fractions

Calculation with complex numbers

» Geometry

Right-angled Triangles

Given two of the elements of a right-angled triangle the others are calculated.

Triangles by three Elements or Points

Given three elements or three points of any triangle the program calculates the sides, altitudes, medians, bisectrices, circumcircle, incircle, perimeter and area.

Regular Polygones

Given one of the following elements of a polygone with n vertices, the others are calculated.

Side, Circumcircle, Incircle, Perimeter and Area.

Arbitrary Polygones

Area, perimeter and centroid of a polygone are calculated

Mappings of Polygones

A polygone can be mapped by a translation, axial symmetry, point symmetry, rotation, homothetic stretching, shear transformation or any combination of them.

Circles and its Parts

Given two elements of a circular section, radius, angle, arc, chord, section, segment, area, perimeter, distance between chord and arc and the arrow height are calculated..

Coordinate Systems

Transformation between cartesian coordinates, polar coordinates and cylindrical coordinates.

Platonic Bodies

Calculates all elements of a Tetrahedron, a Hexahedron, a Octahedron, a Dodekahedron or a Icosahedron

Other Bodies

Calculates all elements of a Regular Prism, a Right Circular Cylinder, a Regular Pyramid, a Right Circular Cone or a Sphere.

Line through two Points

Two points determine a straight line. Its equation will be formed and its position to the co-ordinate planes are analysed.

Plane through three Points

Three non-kollinear points determine a plane. The equation of this plane is formed as Point-slope-form and as Equation in coordinates. The distance from origin and the Trace Points is calculated.

Sphere through four Points

Four non-coplanar points determine a sphere. The equation of this sphere is formed.

Intersections in the Plane

The intersections between two lines, a line and a circle and between two circles are calculated.

Intersections in the Space

The intersections between two lines, a line and plane, two planes, a line and a sphere, a plane and a sphere and between two spheres are calculated.

Distances

The distance between two points, a point and line, a point and a plane, between two lines, a line and a plane and between two planes are calculated.

» Analysis

Division of Polynomials

The product and quotient of two polynoms will be calculated.

Function Plotter

There are three plotters. One for up to five explizit functions, one for segmentwise defined functions and one for functions in parametric representation.

Curve Discussion

Curve discussion of an arbitrary function. The derivations, zeros, extrema and points of inflection are determined.

Newton-Iteration

Approximation of the zeros of a function f(x) by Newton's method with a first guess x0.

Series Expansion

Plotter for functions given as a series over f(x,k). You may develop the function with different parameter ranges and different y-offset.

Integral Calculus

The definite integral over f1-f2 from a to b is calculated as well as the oriented and absolut content under the curve, the twisting moments, the bodies of revolution and the centroid.

Area Functions

Plotter for an area function f(x,y), which may contain a subterm u(x,y).

» Stochastics

Statistics

Mean, median, standard deviation and variance of a sample and the corresponding histogram are calculated.

Regression

The regression curve to fit a sample of points is calculated. Supported are proportional regression, linear regression, geometrical regression, exponential regression, logarithmic regression and polynom regression

Combinatorial Analysis

The number of arrangements and combinations of k out of n elements, with or without repetitions are calculated.

Binomial Distribution

For a b(k;n;p) distributed random variable X with fixed n and p you receive a histogram of the probabilities P( X = k ), a table of their values from kmin to kmax and the probability P(kmin≤X≤kmax).

Hypergeometric Distribution

For a h(k,n,m,r) distributed random variable X with fixed n, m and r you receive a histogram of the probabilities P( X = k ), a table of their values from kmin to kmax and the probability P(kmin≤X≤kmax).

Normal Distribution

For a normal distributed random variable X with given mean μ and variance σ you receive the density function and the distribution function.

» Linear Algebra

Systems of Linear Equations

The solution of a system of linear equations will be calculated.

Linear Combination

The linear combination of a vector out of three linearly independent vectors is determined.

Scalar Product

Given two vectors the scalar product, the length of the vectors and the included angle are calculated.

Vector Product

Given two vectors the vector product and magnitude are calculated.

Triple Product

Given three vectors the mixed product is calculated.

Matrix Inversion

A square matrix of order n is inverted

Matrix Multiplication

Given two matrices A1 and A2 the product matrix is calculated.

**Home Page**- www.matheass.de