MatheAss 9.0  News
MatheAss is also revised from time to time between updates, mostly based on user instructions. With version 9.0 a new version is now available with many new functions.
What's new in MatheAss 9.0?
The following program parts have been added:
Algebra
 Prime tuples
 In an interval [a,b], all prime twins (p,p+2), prime cousins (p,p+4), sexy primes (p,p+6) and prime triplets are determined.
 Calculating percentages
 The base value G, the percentage value W, the percentage p or p%, the growth factor q and the final value E are calculated if two independent values are entered.
 Calculation with big integers (since april 2021)
 Calculation with two big integers a and b with a maximum of 10,000 digits.
 Special straight lines in a triangle
 The program determines the equations of the perpendiculars, the bisectors of the sides, the bisectors of the angles and the heights of a triangle. In addition, the centers and radii of the circumference, the inscribed circle and the three excircles.
 Mappings of Polygons

Displacement, straight line mirroring, point mirroring, rotation, centric stretching and shear can be applied to an ngon.
The input has been made clearer and the construction lines can be drawn in the diagram.  Tangent lines to circles (since february 2021)
 The following tangents will be calculated:
 The tangent to a circle k at a point B.
 The tangents to a circle k through a point P outside the circle
 The tangents to a circle k parallel to a straight line g
 The tangents to two circles k_{1} and k_{2}
 Distances_on_the_Sphere (since december 2021)
 Sequences and Series (since may 2021)
 The program determines the first n terms of a sequence (a_{i}) and the associated series
(sum of the sequence terms) if the first terms of the sequence and a recourse formula
a_{i}=ƒ(a_{0}, a_{1}, ... , a_{i1})
or an explicit function a_{i} = ƒ(i) are given.
The sequence of odd numbers e.g. can be defined explicitly by a_{i} = 2·i + 1 or recursively by a_{i} = a_{i1} + 2 with a_{0}=1 .  Factoring Polynomials
 The program calculates the rational zeros and the linear factorization of a polynomial.
 Transforming Polynomials
 A polynomial p(x) can be shifted or stretched in the xdirection and ydirection.
 GCD and LCM of polynomials (since february 2021)
 The greatest common divisor (GCD) and the least common multiple (LCM) of two polynomials p_{1}(x) and p_{2}(x) are determined..
 Calculus of Polynomial Functions
 The program carries out the curve discussion for polynomial function. This means that the derivatives and the antiderivative are determined, the function is examined for rational zeros, for extremes, for inflection points and for symmetry.
 Calculus of Rational Functions
 The program carries out the curve discussion for a rational function. That is, the derivatives, the definition gaps and the continuous continuation are determined. The function is examined for zeros, extrema, points of inflection: and the behavior for  x  → ∞.
 Integralrechnung (since February 2021 with arc lengths)
 Statistics
 In the statistics section, the histogram was supplemented by a box plot.
 Logistic Regression
 The program determines a curve fit for a series of measurements to the logistic function
with the parameters a_{1} = ƒ(0)·S , a_{2} = ƒ(0) , a_{3} = S  ƒ(0) , und a_{4} = k·S and the saturation limit S .  Data series from Johns Hopkins University (JHU) on the corona pandemic are attached as CSV files.
Prime twins between 1 and 200 (35) (57) (1113) (1719) (2931) (4143) (5961) (7173) (101103) (107109) (137139) (149151) (179181) (191193) (197199) 15 pairs of prime twins
Prime triplets between 1 and 100 (357) (5711) [71113] (111317) [131719] (171923) [374143] (414347) [677173] 9 triplet prime triplets 4 of the form (pp+2p+6) and 4 of the form [pp+4p+6]
Given: ¯¯¯¯¯¯ basic value G = 150 percentage p% = 2.5% = 0.025 = 1/40 Results: ¯¯¯¯¯¯¯ percentage value W = 3.75 growth factor q = 102,5% = 1,025 = 41/40 final value E = 153.75
Given: ¯¯¯¯¯¯ percentage value W = 120 growth factor q = 95% = 0,95 = 19/20 Results: ¯¯¯¯¯¯¯ basic value G = 2400 percentage p% = 5% = 0.05 = 1/20 final value E = 2280
Geometry
Given: ¯¯¯¯¯¯ Edges: A(10) B(51) C(36) Results: ¯¯¯¯¯¯¯ Vertices: a : 5·x + 2·y = 27 b : 3·x  y = 3 c : x  4·y = 1 Incircle: Mi(3,1191,962) r i = 1,390 Excircles: Ma(7,6266,136) ra = 4,346 Mb(4,3565,784) rb = 6,910 Mc(3,2482,427) rc = 2,900
Counter image A(11), B(51), C(55), D(37), E(15), 1. Translation: dx=2, dy=1 ☑ A(32), B(72), C(76), D(58), E(36), 2. Rotation: Z(21), α=60° ☑ A(5,09810,36603), B(7,09813,8301), C(10,5621,8301), D(11,2940,90192), E(8,56221,634),
Given: ¯¯¯¯¯ k_{1} : M(58) , r =5 k_{2} : M(12) , r =3 Outer tangents ¯¯¯¯¯¯¯¯¯¯¯¯ t_{1}: 4,2923·x + 7,04104·y = 6,36427 t_{2}: 7,04104·x + 4,29230·y = 40,3643 Inner tangents ¯¯¯¯¯¯¯¯¯¯¯¯ t_{3}: 1,21895·x + 2,55228·y = 12,3709 t_{4}: 2,55228·x  1,21895·y = 8,3709
GPS decimal ¯¯¯¯¯¯¯¯¯¯¯ Berlin : 52.523403, 13.4114 New York : 40.714268, 74.005974 GPS dms ¯¯¯¯¯¯¯ Berlin : 52° 31' 24.2508" N, 13° 24' 41.0400" E New York : 40° 42' 51.3648" N, 74° 0' 21.5064" W . . . Distance ¯¯¯¯¯¯¯¯¯¯ d = r · α [rad] = 6385,112
Analysis
Folge ¯¯¯¯¯ ( a[ i ] ) = (1; 3; 5; 7; 9; 11; 13; 15; 17; 19) Reihe ¯¯¯¯¯ ( Σ a[ i ] ) = (1; 4; 9; 16; 25; 36; 49; 64; 81; 100)
p(x) = x^{5}  9·x^{4}  82/9·x^{3} + 82·x^{2} + x  9 = (1/9)·(9·x^{5}  81·x^{4}  82·x^{3} + 738·x^{2} + 9·x  81) = (1/9)·(3·x  1)·(3·x + 1)·(x  9)·(x  3)·(x + 3) Rational Zeros: 1/3, 1/3, 9, 3, 3
ƒ(x) =  1/4·x^{4} + 2·x^{3}  16·x + 21 Shifted by dx = 2 , dy = 0 ƒ(x + 2) =  1/4·x^{4} + 6·x^{2} + 1
p_{1}(x) = 4·x^{6}  2·x^{5}  6·x^{4} 18·x^{3}  2·x^{2} + 24·x + 8 p_{2}(x) = 10·x^{4} 14·x^{3}  22·x^{2} + 14·x + 12 GCD(p_{1},p_{2}) = x^{2}  x  2 LCM(p_{1},p_{2}) = 40·x^{8}  36·x^{7}  76·x^{6}  144·x^{5} + 88·x^{4}+ 356·x^{3}  4·x^{2}  176·x  48
Function : ¯¯¯¯¯¯¯¯ ƒ(x) = 3·x^{4}  82/3·x^{2} + 3 = 1/3·(9·x^{4}  82·x^{2} + 9) = 1/3·(3·x  1)·(3·x + 1)·(x  3)·(x + 3) Derivations : ¯¯¯¯¯¯¯¯¯¯ ƒ'(x) = 12·x^{3}  164/3·x ƒ"(x) = 36·x^{2}  164/3 ƒ'"(x) = 72·x Antiderivative: ¯¯¯¯¯¯¯¯¯¯¯¯ ƒ(x) = 3/5·x^{5}  82/9·x^{3} + 3·x + c …
Function : ¯¯¯¯¯¯¯¯ 3·x^{3} + x^{2}  4 (x  1)·(3·x^{2} + 4·x + 4) ƒ(x) = —————— = ——————————— 4·x^{2}  16 4·(x  2)·(x + 2) Definition gaps : ¯¯¯¯¯¯¯¯¯¯¯¯¯ x = 2 Pol mit Vorzeichenwechsel x =2 Pol mit Vorzeichenwechsel Derivations : ¯¯¯¯¯¯¯¯¯¯ 3·(x^{4}  12·x^{2}) 3·(x^{2}·(x^{2}  12)) ƒ'(x) = ———————— = ————————— 4·(x^{4}  8·x^{2} + 16) 4·(x  2)^{2}·(x + 2)^{2} 6·(x^{3} + 12·x) 6·(x·(x^{2} + 12)) ƒ"(x) = ——————————— = ———————— x^{6}  12·x^{4} + 48·x^{2}  64 (x  2)^{3}·(x + 2)^{3} …
ƒ_{1}(x) = cosh(x) ƒ_{2}(x) = x^2+1 Limits of integration [a;b] from 2 to 2 Oriented content : A_{1} = 2,07961 Absolute content : A_{2} = 2,07961 Arc lengths : L_{1}[a;b] = 7,254 L_{2}[a,b] = 9,294
Stochastics
Data from: "hopfenwachstum.csv" Saturation limit: 6 Dark figure: 1 4,0189 ƒ(x) = ———————————————— 0,66981 + 5,3302 · e^(0,35622·t) Inflection point W(5,8226/3) Maximum growth rate ƒ'(xw) = 0,53433 8 Values Coeff.of determin. = 0,99383916 Correlation coeff. = 0,99691482 Standard deviation = 0,16172584
Linear Algebra
Objective function: ƒ(x,y) = 140·x + 80·y → Maximum Constraints: x ≥ 0 y ≥ 0 x ≤ 600 y ≤ 700 x + y ≤ 750 3·x + y ≤ 1200 Maximum x = 225 y = 525 ƒ(x,y) = 73500
Registration
How much costs MatheAss 9.0?
29 € for the private license
79 € for the school license
360 € for the extended school license, with which the serial number may be passed on to the pupils.
How much is the update?
10 € for owners of a private license
30 € for owners of a school license
90 € for owners of an extended school license
How can I pay?
Here by PayPal :
← open here to select the desired license