JavaScript    (On Mathematics Education)       (see here for charts in PHPhere with Desmoshere with R)     → Wolfram

  Per le scuole       Basic School Scripts

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percentage × table numbers sum/ratios mean
division triangle (1) Pythagoras circle pocket c.
commands ex. sorting manipulation quizzes / tree block diagr.0-3
pie chart strip/bar graphs/% drawing 360/100/180/mm various graphics
sequences graphs h - min fractions a die - 2 dice histogram
divisors prime fatc./numb. simpl.fract./gcd decim./ratio + × integers
prop. transf. simple eq. rounding polyg./area ... barycenter
∠ABC triangle (2) circle tangent 2 p./vector
line/line dist. P-line circle/circle Pr(x+y<k), ... approx.1
approx.2 tab.polin. pocket c. 2 boxplot boxplot 2
boxplot 3 factorial 1 factorial 2 distance in R^2 circle arcs / sin
lin.system 2/3 determinant lin.system 4 matrix multipl. 2 seq./vectors
binom.coeff. sq./cube root how many steps en/decode reorder quiz
divis.base≠10 repeated diff. funct.(tab/limit) recurs.def. series
integral pol. integral Gauss pol. mult/pol.equation equation max/min of pol.
max/min of fun. random number time × matr. deriv. of fun. integral of fun.
Attention! prob. of events dist. P/curve - curve arc lenght lin/qua/cub regress.
extract subtable test χ² distance in R^3 arc 3D lenght transf. seq.
tab. of fun. dist. on sphere calculations a magic square ex. of integrated uses

percentuali    percentage     (examples-esempi)

tabellina / × table (1-9)    1-12    1-12*    1-31     (remarks and examples-note ed esempi)

integers / numeri interi     (examples-esempi)

decimals / numeri decimali     (examples-esempi)

approximations / approssimazioni

sums and ratios  /  somme e rapporti     (examples-esempi)

mean  /  media     (examples-esempi)

division  /  divisione    (examples-esempi)

rapporto  tra due numeri (interi o no) espresso anche in forma percentuale / ratio  between two (whole or not) numbers, also in percentage form (esempi/examples)

area triangle,parallelogram / triangolo,parallelogramma

sum angles of triangle / somma angoli di un triangolo

angles/sides/area of a triangle / angoli/lati/area di un triangolo

Pythagoras Theorem / Teorema di Piatgora

perimeter/area of the circle / perimetro/area del cerchio

first calculator / prima calcolatrice

pocket calculator  /  calcolatrice    (examples-esempi)

pocket calculator - calcolatrice - 1    (examples-esempi)

use of array, write, writlen, for, if    (an example/un esempio)

use of function, form, input / uso di  . . .    (example-esempio)

sorting numbers / ordinamento di numeri    (examples/esempi)

Expression manipulation, Constants: examples that can be helpful (formule e costanti).

preparation and administration of quizzes / preparazione e somministrazione di quiz


tree diagrams

block diagrams - 0  /  diagrammi a barre - 0    (examples-esempi)

block diagrams - 1  /  diagrammi a barre - 1    (examples-esempi)

block diagrams - 2  /  diagrammi a barre - 2    (examples-esempi)

block (crosses) diagrams - 3  /  diagrammi a barre (a crocette) - 3    (examples-esempi)

pie chart / diagrammi a torta    (examples/esempi)

strip diagrams  /  diagrammi a striscia  (figure on the right)    (examples-esempi)

other bar graphs  /  altri grafici a barre    (examples-esempi)

bar graphs (of functions) / grafici a barre (di funzioni)    (examples-esempi)

disegnare (1) (come si disegna col computer?) / drawing (1) (how is a drawing done with a computer?)

  disegnare (2) / drawing (2)

  Disegnare su carta quadrettata col computer
  How to draw on squared paper

  disegnare (3) / drawing (3)  new version

  Disegnare su carta quadrettata col computer - bis
  How to draw on squared paper - bis

  disegnare (4) / drawing (4)  new version

(disegnare col computer su carta quadrettata / senza quadretti - per l'insegnante)
How to draw (using the computer) on squared paper /paper without squares (for the teacher)

  disegnare (5) / drawing (5)  new version
(disegnare col computer su carta quadrettata / senza quadretti - per l'insegnante - formato maggiore)
How to draw (using the computer) on squared paper /paper without squares (for the teacher - larger size)


360-100-180   (in PHP)

carta millimetrata / graph paper

Un "foglio" di carta millimetrata per costruire (a mano)
grafici di funzioni "sperimentali" (come il peso di una
persona al passare degli anni) o espresse da formule.

A "sheet" of graph paper to build (by hand) graphs of
"experimental" functions (such as the weight of a person
over the years) or functions expressed by formulas.

range di una funzione / of a function     (esempi / examples)

grafici semplici / simple graphs (functions, figures)  in dimensioni minori / in smaller size   molto minori / much smaller   (esempi / examples)

various graphics (and animations)

parabole (e rette) / parables (and lines)
  in dimensioni minori / in smaller size

            iperboli / hyperbolas
  in dimensioni minori / in smaller size

            cerchi / circles

                        ellissi / ellipses

iperboli (anche per x<0) / hyperbolas (even for x<0)
          in dimensioni minori / in smaller size

grafici di successioni / sequences graphs      

h - min    (examples)

fractions / frazioni    (examples-esempi)

a die / un dado   (random)    (examples)

2 dice  /  2 dadi  (random)    (examples)

histogram (starting from single data)    (examples)
histogram with tighter rectangles

divisors  /  divisori    (examples)

prime factors  /  prime factors - 2    (examples)

prime number     (examples)

simplifying fractions  (GCD / MCD)    (examples)

d  →  m/n  (repeating decimal → ratio of integers  /  numero periodico → rapporto tra interi)


calculations with anyway large integers / calcoli con interi comunque grandi   (examples)

proportional transformation of data    (examples)

solve simple equations / semplici equazioni    (examples)

rounding  /  arrotondamento    (examples/esempi)

area and center (and perimeter)  /  area e centro (e perimetro)    (example, with PHP / Desmos graph)

barycenter in the plane

barycenter in the space

angle ABC  /  angolo ABC    (examples)

triangle (if I know 3 Sides/Angles, se conosco 3 lati/angoli)

Drawing a triangle  /  Disegno di un triangolo

circle that passes through 3 points    (examples)


circle inscribed in a triangle

center/radius of a circle    (examples)


Tangents to a circle passing through a point P    (examples)

2 points in the plane (vector)    (examples)


intersection of 2 straight lines     (examples)

distance between a point and a line     (examples)

intersection of 2 circles     (examples)

x+y < k, if x,y ∈ [0,1]  and  other examples  of probability of events and distribution laws

approximations - interval arithmetic - intervalli d'indeterminazione     (examples)

approximations of generic functions (of 1,…,4 variables)

tabulating polinomial function    (examples)

pocket calculator - 2    (examples)

boxplot    (examples)

boxplot comparison    (examples)

boxplot of classified data    (examples)

factorial (!)     fattoriale (!)

factorial (!)    (examples)


length of circle arcs

the function sine

linear system - 2 equations

linear system - 3 equations    (examples)

determinant 3x3    determinant 4x4    determinant 5x5    determinant 6x6

linear system - 4 equations (and determinant 4x4)    (examples)

matrix multiplication    (examples)

2 sequences / vectors    (examples)

binomial coefficient   (see also ↑ "pocket calc. 2")

square root and cube root    (see also "recursive definitions" below)

How many steps? / Quanti passi?
How many steps? - more / Quanti passi? - bis

encode / decode    (examples)

change the order of quizzes    (examples-esempi)

division in a base of your choice    (examples)

division of m by n with m < n (natural numbers in base ten) and result in a base of your choice
By clicking  [one step]  you gradually get the figures of the result
m = n = base =
remainder =    

division of m by n with m < n (natural numbers in base ten) and result in a base of your choice
By clicking  [one step]  you gradually get the figures of the result
m = n = base =
remainder =    

repeated differences    (examples)

tabulation of a function  (and calculation of limits)   (examples)
[Now  x →  sin(x)/x  is calculated]

recursive definition    (examples)
[Now  F(1) = 1, F(n+1) = 2· F(n)  is calculated]

series    (examples)
[Now the sum 1 + 0.8 + 0.8² + 0.8³ + ... is calculated]

integral of a polynomial function (raised to a real exponent)    (examples)

integral of Gauss distribution    (examples)

multiplication of polynomials

solve polinomial equations F(x)=0    (examples)

solve equations F(x)=0    (examples)

max of polinomial fun. in [a,b]

min of polinomial fun. in [a,b]    (examples)

max F in [a,b]    (examples)
[Now F is  x^4 + 5*x^3 - 20*x + 2]


min F in [a,b]    (examples)
[Now F is  x^4 + 5*x^3 - 20*x + 2]


random number generation    (examples)

time to multiply N×N matrices    (examples)

derivative of functions    (examples)
[Now the function is x → x³+1]

integrals of functions    (examples)
[Now the integral of x → √(x³+1) - between 1 and 7 - is calculated]

the concept of limit: attention! / il concetto di limite: attenzione!

the concept of continuity: attention! / il concetto di continuità: attenzione!

probability of events    (examples)

distance of a point P from a curve x=x(t), y=y(t)   (examples)

distance between two curves P=P1(t1) and P=P2(t2)   (examples)

arc lenght   (examples)

linear regression   (examples)

quadratic regression   (examples)

cubic regression   (examples)

how to extract a subtable   (examples)

χ² (Chi-squared test)   (examples)

2 points in the space   (examples)

arc 3D lenght    (example)

transformation of data sequences   (examples)

automatic tabulation of a function (for various uses)   (examples)

orthodromic distance (distance between 2 points on a sphere)   (examples)

calculations    (example)         calculations2    (example)         calculations3    (example)

calcolo di F(x)     calcolo di F(x,y)     calcolo di F(x,y,z)

a magic square  /  un quadrato magico    (examples-esempi)

Examples of integrated uses of various scripts


( # ) Se usi un Mac, ti conviene usare un qualunque browser (Edge, Firefox, Opera, …) diverso da Safari, che non riconosce "with(Math)" in alcuni file in JavaScript. Comunque, i file qui presenti sono stati modificati in modo da funzionare anche in Safari (se ci sono problemi scrivete). Se vuoi modificare un file e non riesci a visualizzare il sorgente con un Mac, modfica l'estensione da "htm" a "txt", apri il file con TextEdit, modicalo e rimetti l'estensione "htm".  /  If you use a Mac, you should use any browser (Edge, Firefox, Opera, ...) other than Safari, which doesn't recognize "with(Math)" in some JavaScript files. However, the files here have been modified to work in Safari too (if there are any problems write). If you want to edit a file and you can't view the source with a Mac, change the extension from "htm" to "txt", open the file with TextEdit, edit it and put the extension "htm" back.