miércoles, 24 de junio de 2026

geometría-diferencial y arte-matemático

Teorema:

Sea H_{kk}^{k} = k ==> 

x_{k}(t) = (1/k)·ln(t)

Si d_{t}[x_{s}]^{2} = ( x_{s} )^{2} ==>

x_{s}(t) = e^{t}

R_{ijs}^{sss} = ij·t^{2}·e^{2t}

Teorema:

Sea H_{kk}^{k} = k ==> 

x_{k}(t) = (1/k)·ln(t)

Si d_{t}[x_{s}] = x_{s} ==>

x_{s}(t) = e^{t}

R_{ssk}^{sss} = kt·e^{t}


Teorema:

Sea H_{kk}^{k} = kt ==> 

x_{k}(t) = (2/k)·(-1)·(1/t)

Si d_{t}[x_{s}]^{2} = ( x_{s} )^{n} ==>

x_{s}(t) = ( (1+(-1)·(1/2)·n)·t )^{( 1/(1+(-1)·(1/2)·n) )}

R_{ijs}^{sss} = ij·(1/4)·t^{4}·( (1+(-1)·(1/2)·n)·t )^{( n/(1+(-1)·(1/2)·n) )}

Teorema:

Sea H_{kk}^{k} = kt ==> 

x_{k}(t) = (2/k)·(-1)·(1/t)

Si d_{t}[x_{s}] = ( x_{s} )^{n} ==>

x_{s}(t) = ( (1+(-n))·t )^{( 1/(1+(-n)) )}

R_{ssk}^{sss} = k·(1/2)·t^{2}·( (1+(-n))·t )^{( n/(1+(-n)) )}


Arte:

[En][ sum[k = 1]-[n][ mcd{km,k} ] = n ]

Exposición:

n = 1

f(k) = 1

sum[k = 1]-[n][ mcd{km,k} ] = sum[k = 1]-[n][ mcd{f(k)·m,f(k)} ] = ...

... sum[k = 1]-[n][ mcd{m,1} ] = sum[k = 1]-[n][ 1 ] = n

Arte:

[En][ sum[k = 1]-[n][ mcm{km,k} ] = nm ]

Exposición:

n = 1

f(k) = 1

sum[k = 1]-[n][ mcm{km,k} ] = sum[k = 1]-[n][ mcm{f(k)·m,f(k)} ] = ...

... sum[k = 1]-[n][ mcm{m,1} ] = sum[k = 1]-[n][ m ] = nm