JavaScript    (On Mathematics Education)     (see here for charts in PHP,  here with Desmos,  here 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.
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 (examples-esempi)

scientific notation / notazione scientifica

approximations / approssimazioni

radice quadrata    square root

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 - 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

istogrammi introducendo tutti i dati histograms by introducing all data  rettangoli più stretti / tighter rectangles

(esempi)

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

LAPIS  /  PEN 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)

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? click

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)

5.3627627627627... → 8929/1665

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)

distance

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             (examples)

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)

Escher

Examples of integrated uses of various scripts

un gioco / a game

programmare / coding  in  JavaScript programming / coding   in  JavaScript

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.