geometria borrosa

Triangles pitagórics iscrits en una circuferència:


P(n) = (1/2)·( (2n+1)^{(1/2)}·n )/( (n+1)^{2}·pi)


(2n+1)+n^{2} = (n+1)^{2}

constructor matemàtic borrós dos daus

en dos daus:


p=q


1=1
2=2
3=3
4=4
5=5
6=6


p( p=q ) = (6/36) = (1/6)


p+q=2


1+1=2


P( p+q=2 ) = (1/36)


p+q=12


6+6=12


P( p+q=12 ) = (1/36)


p+q=3


1+2=3
2+1=3


P( p+q=3 ) = (2/36) = (1/18)


p+q=11


5+6=11
6+5=11


P( p+q=11 ) = (2/36) = (1/18)


p+q=4


1+3=4
2+2=4
3+1=4


P( p+q=4 ) = (3/36) = (1/12)


p+q=10


4+6=10
5+5=10
6+4=10


P( p+q=10 ) = (3/36) = (1/12)


p+q=5


1+4=5
2+3=5
3+2=5
4+1=5


P( p+q=5 ) = (4/36) = (1/9)


p+q=9


3+6=9
4+5=9
5+4=9
6+3=9


P( p+q=9 ) = (4/36) = (1/9)


p+q=6


1+5=6
2+4=6
3+3=6
4+2=6
5+1=6


P( p+q=6 ) = (5/36)


p+q=8


2+6=8
3+5=8
4+4=8
5+3=8
6+2=8


P( p+q=8 ) = (5/36)


p+q=7


1+6=7
2+5=7
3+4=7
4+3=7
5+2=7
6+1=7


P( p+q=7 ) = (6/36) = (1/6)

índex de matemàtiques

index de etiquetes matemàtiques

derivada imperial

d_{x}^{(1/m)}[x^{n}] = n^{(1/m)}·x^{( (n+(-1))/m )}
d_{x}^{(1/m)}[e^{x}] = e^{(1/m)x}


d_{t}^{(1/m)}[ d_{t}^{(1/m)}[x(t)]^{m} ] + ( a^{(2/m)}( x(t) )^{(1/m)} ) = 0 <==> x(t)=e^{at·i}


d_{x}^{(1/m)}[ f(x)+g(x) ] =[2/2^{m}]= d_{x}^{(1/m)}[f(x)] + d_{x}^{(1/m)}[g(x)]
d_{x}^{(1/m)}[ af(x) ] = a^{(1/m)}·d_{x}^{(1/m)}[f(x)]


d_{x}^{(1/m)}[ ax^{2}+bx ] =[2/2^{m}]= (2ax)^{(1/m)} + b^{(1/m)}


d_{x}^{(1/m)}[ ax^{3}+bx^{2}+cx ] =[3/3^{m}]= (3a)^{(1/m)}·x^{(2/m)}+(2bx)^{(1/m)}+c^{(1/m)}

constructor matemàtic borrós geometria

P(b)= (1/3)·int[ b+(-x) ]d[x] [M] int[ b^{2}+(-1)x^{2} ]d[x] = ( (b^{2})/(b^{3}) ) = (1/b)

constructor matemàtic borrós geometria

cercle inscrit en un cuadrat
P(a)= pi·r^{2} [M] (2r)^{2} = ( pi/4 )


cercle inscrit en una creu de 5 cuadrats
P(a)= pi·r^{2} [M] 5·(2r)^{2} = ( pi/20 )


4 cercles inscrits en una creu de 5 cuadrats
P(a)= 4·pi·r^{2} [M] 5·(2r)^{2} = ( pi/5 )


esfera inscrita en un cub
P(a)= (4/3)·pi·r^{3} [M] (2r)^{3} = ( pi/6 )


esfera inscrita en una poli-creu de 7 cubs
P(a)= (4/3)·pi·r^{3} [M] 7·(2r)^{3} = ( pi/42 )


6 esferes inscrites en una poli-creu de 7 cubs
P(a)= 6·(4/3)·pi·r^{3} [M] 7·(2r)^{3} = ( pi/7 )

constructor matemàtic borrós geometria

triangle equiláter circumscrit en un cercle
P(a)= (1/2)·2r sin(pi/6)·2r·cos(pi/6) [M] pi·r^{2} = ( 3^{(1/2)}/(2pi) )


cuadrat equiláter circumscrit en un cercle
P(a)= 2r sin(pi/4)·2r·cos(pi/4) [M] pi·r^{2} = ( 2/pi )