JavaScript    (On Mathematics Education)     (see here for charts in PHPhere with Desmoshere with R)    → WolframAlpha
grafici/graphs  con/with WolframAlpha

  Per le scuole       Basic School Scripts     (per l'insegnamento della fisica   for teaching physics)

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percentage / first eq × table numbers   √  + × /   mean division/slope
graphs/animations triangle (1) Pythagoras circle pocket c.  (new)
commands ex. sorting manipulation quizzes / tree block diagr.0-3
pie chart strip/bar graphs/% drawing  /  colors 360/100/180/mm various graphics
sequences graphs h - min fractions coin - die-dice - prob.(1) histogram
divisors prime fatc./numb. simpl.fract./gcd decim./ratio + × integers
prop. transf. various equations rounding polyg./area/centroid... barycenter
∠ABC triangle (2) circle tangent 2 p./vector
line/line dist. P-line circle/circle Pr(x+y<k),Rnd+Rnd,... 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 determinant 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 min / max / flex max/min of pol.
max/min of fun. random num./ exercises time × matr. deriv. of fun. integral of fun.
Attention! prob. of events (2) dist. P/curve - curve arc lenght lin/qua/cub regres.
extract subtable test χ² distance in R^3 arc 3D lenght transf. seq.
dist. on sphere moving mean tab. of fun. calculations a magic square
Escher ex. of integrated uses a game / coding

percentuali    percentage     (examples-esempi)

distribuzioni percentuali - percentage distributions   (5,4,3,2,1,0 cifre dopo unità - digits after units)
distribuzioni percentuali3 - percentage distributions3   (3 cifre dopo unità - 3 digits after units)
distribuzioni percentuali2 - percentage distributions2       (2 cifre dopo unità - 2 digits after units)
distribuzioni percentuali1 - percentage distributions1   (1 cifra dopo unità - 1 digits after units)
distribuzioni percentuali0 - percentage distributions0   (0 cifra dopo unità - 0 digits after units)

first equations (A)   first equations (B)   first equations (C)   first equations (D)
prime equazioni (A)   prime equazioni (B)   prime equazioni (C)   prime equazioni (D)

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

integers / numeri interi   (+1   -1)       

integers / numeri interi     (examples-esempi)


  +   −  

(or    +   −  )

che numero è? / what number is it?

che numero è? / what number is it?



integers     (examples)

numeri interi     (esempi)



integers*     (examples)



decimals / numeri decimali



scientific notation / notazione scientifica   


approximations / approssimazioni   


radice quadrata

   square root


somma / moltiplica  /  sum / product

qual è il risultato  /  what is the result?

A / B  

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)

rapporto tra due aree  /  ratio between two areas

rapporto tra due colonne  /  ratio between two columns

pendenza  /  slope

cerchio  /  circle

parabola  /  parable

area triangoli  /  area triangles

area quadrangoli  /  area quadrangles

symmetry / simmetria

a theorem / un teorema   (see/vedi)

area triangle,parallelogram / triangolo,parallelogramma

area di semplici quadrilateri / of simple quadrilaterals

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   (help)

RPN calculator /calcolatrice a notazione postfissa

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)

metti in ordine alfabetico
put in alphabetical order
metti in ordine numerico
put in numerical order

sorting numbers - 1 / ordinamento di numeri - 1

sorting numbers ← / ordinamento di numeri ←

sorting numbers - 2 / ordinamento di numeri - 2    (examples/esempi)

  ordering of words - 1 / ordinamento di parole - 1
  ordering of words / ordinamento di parole - 2
  written in lowercase characters, separated by commas / scritte in lettere minuscole, separate da virgole.

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 / diagrammi a barre

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

block diagrams + median  /  diagrammi a barre + mediana    (examples-esempi)

istogrammi introducendo tutti i dati
histograms by introducing all data

 rettangoli più stretti / tighter rectangles
semplici istogrammi /simple histograms
    (per l'insegnante / for the teacher)
            esempi / example

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)

empty/vuoto  circle / cerchio divided into cents
    semicircle / semicerchio divided into fiftieths

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

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

bar graphs (of functions/sequences) / grafici a barre (di funzioni/successioni)    (examples-esempi)
bar graphs / grafici a barre   rettangoli più stretti / tighter rectangles

disegnare / drawing

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


disegno (0) / draw (0)
  esempi /examples

disegnare (2) / drawing (2)
  Disegnare su carta quadrettata col computer
  How to draw on squared paper

disegno (1) / draw (1)
disegno (2) / draw (2)

  disegnare (3) / drawing (3)   (old version)

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

  disegnare (4) / drawing (4)   (old 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 (4b) / drawing (4b)   su carta più ampia / on larger paper

  disegnare (5) / drawing (5)   (old 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)


  Polimini / Polyominos

  Isola del tesoro/Treasure Island

Indicare i passi (nelle direzioni N,S,O,E) per giungere al tesoro
Indicate the steps (in the N,S,W,E directions) to reach the treasure.

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)

poligoni / polygons 

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

Come sono fatte le figure in 3 dimensioni?
How are 3D figures made?


grafici di successioni / sequences graphs


 min    (+1   -1)

h - min    (examples)

fractions / frazioni    (examples-esempi)

a coin (heads or tails) / una moneta (T o C)

a die / un dado   (random)    (examples)

un dado non equo / a not balanced die  

2 dice  /  2 dadi  (random)    (examples)

un primo programma per valutare probabilità  -  a first program for finding probabilities   (vedi poi / then see here)

istogramma di dati interi / histogram of integer data
(a partire da dati singoli / starting from single data)    (examples)

(esiti di 50 lanci di un dado / results of 50 rolls of a dice)

istogramma (versione semplificata)  /  histogram (simplified version)
histogram (starting from single - or classified - data)    (examples)
histogram with tighter rectangles - histogram with much 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 various equations / equazioni varie    (examples)

rounding  /  arrotondamento    (examples/esempi)

area and center (and perimeter)  /  area e centro (e perimetro)    (example)
area and center (picture)  /  area e centro (immagine)


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)
intervalli d'indeterminazione     (esempi)

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 in a base of your choice (+ remainder)   (examples)

repeated differences    (examples)

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

recursive definitions    (examples)

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
        (and division)

solve polinomial equations of greater degree

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

min, max, flesso (esercizi)
min, max, inflection (exercises)

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 numbers generation in (0,1)   random numbers generation in (a,b)   (notes)


random integers (but not only integers) generation    (examples)
generatore numeri interi (ma non solo interi) casuali    (esempi)

numbers in [0;1] generation (with seed)    (examples)

random numbers generation in [a,b]    (examples)

random integers generation from a to b    (examples)

random different integers generation from a to b    (examples)

numbers from 1 to 99 generation    (examples)

random data generation    (example)

Random  derivative of polynomials   derivative of f(x)/g(x)   derivative of f(g(x))


gaussian number generation

cube of gaussian number generation

negative exponential distribution generation     (example)

Poisson distribution generation     (example)

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]

integrals of functions whose antiderivative is not known  (you can also use ↑)
sqrt(1+x^3)  1/sqrt(1+x^4)  1/log(x)  sin(x)/x  sin(x^2)  exp(x)/x  exp(x^2)  cos(exp(x))  sqrt(1-x^4)  exp(-x^2)  exp(-x)/x  exp(exp(x))  log(log(x))  sin(1/x)  exp(x)·sin(x)/(1+x^2)

programma per integrare generiche funzioni (p10)  -  program to integrate generic functions (p10)

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

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

probability of events    (examples)

programma per calcolare probabilità  -  program for calculating probabilities

distance between 2 ellipses  (examples)         distance between an ellipse and a line  (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)

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

moving mean - medie mobili  (examples)

automatic tabulation of a function (for various uses)   (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

un gioco / a game
programmare / coding  in  JavaScript
programming / coding   in  JavaScript


( # ) 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.