La cruz en la multiplicación
Esta formación numérica básica la encontramos en nuestra vida cotidiana en todos los teléfonos, mandos de control remoto, ordenadores y sistemas de adquisición de datos.
5.1.1. Tabla del uno.
( V ) = 258 x 360 = 92.880
( Vinv ) = 852 x 360 = 306.720
( V + Vinv ) = 92.880 + 306.720 = 399.600
( H ) = 456 x 360 = 164.160
( Hinv ) = 654 x 360 = 235.440
( H + Hinv ) = 164.160 + 235.440 = 399.600
Dado que en la matriz dada existen
dos cruces :
5.1.2. Tabla del uno.
( D1 ) = 753 x 360 = 271.080
( D1inv ) = 357 x 360 = 128.520
( D1 + D1inv ) = 271.080 + 128.520 = 399.600
( D2 ) = 951 x 360 = 342.360
( D2inv ) = 159 x 360 = 57.240
( D2 + D2inv ) = 342.360 + 57.240 = 399.600
X inv : Variable invertida.
5.2. Tabla del dos
( V ) = 4 + 10 + 16 = 30
( H ) = 8 + 10 + 12 = 30
( D1 ) = 2 + 10 + 18 = 30
( D2 ) = 6 + 10 + 14 = 30
( V ) = 4 + ( 1 + 0 ) + ( 1 + 6 ) = 12
( H ) = 8 + ( 1 + 0 ) + ( 1 + 2 ) = 12
( D1 ) = 2 + ( 1 + 0 ) + ( 1 + 8 ) = 12
( D2 ) = 6 + ( 1 + 0 ) + ( 1 + 4 ) = 12
5.3. Tabla del tres.
( V ) = 6 + 15 + 24 = 45
( H ) = 12 + 15 + 18 = 45
( D1 ) = 3 + 15 + 27 = 45
( D2 ) = 9 + 15 + 21 = 45
( V ) = 6 + ( 1 + 5 ) + ( 2 + 4 ) = 18
( H ) = (1 + 2 )+ ( 1 + 5 ) + ( 1 + 8 ) = 18
( D1 ) = 3 + ( 1 + 5 ) + ( 2 + 7 ) = 18
( D2 ) = 9 + ( 1 + 5 ) + ( 2 + 1 ) = 18
5.4. Tabla del cuatro.
( V ) = 8 + 20 + 32 = 60
( H ) = 16 + 20 + 24 = 60
( D1 ) = 4 + 20 + 36 = 60
( D2 ) = 12 + 20 + 28 = 60
( V ) = 8 + ( 2 + 0 ) + ( 3 + 2 ) = 15
( H ) = (1 + 6 )+ ( 2 + 0 ) + ( 2 + 4 ) = 15
( D1 ) = 4 + ( 2 + 0 ) + ( 3 + 6 ) = 15
( D2 ) = (1 + 2 ) + ( 2 + 0 ) + ( 2 + 8 ) = 15
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10
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15
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20
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25
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30
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35
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40
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45
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5.5. Tabla del cinco.
( V ) = 10 + 25 + 40 = 75
( H ) = 20 + 25 + 30 = 75
( D1 ) = 5 + 25 + 45 = 75
( D2 ) = 15 + 25 + 35 = 75
( V ) = (1 + 0) + ( 2 + 5 ) + ( 4 + 0 ) = 12
( H ) = (2 + 0 )+ ( 2 + 5 ) + ( 3 + 0 ) = 12
( D1 ) = 5 + ( 2 + 5 ) + ( 4 + 5 ) = 21
( D2 ) = (1 + 5 ) + ( 2 + 5 ) + ( 3 + 5 ) = 21
6
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12
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18
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24
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30
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36
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42
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48
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54
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5.6. Tabla del seis.
( V ) = 12 + 30 + 48 = 90
( H ) = 24 + 30 + 36 = 90
( D1 ) = 6 + 30 + 54 = 90
( D2 ) = 18 + 30 + 42 = 90
( V ) = (1 + 2 ) + ( 3 + 0 ) + ( 4 + 8 ) = 18
( H ) = (2 + 4 ) + ( 3 + 0 ) + ( 3 + 6 ) = 18
( D1 ) = 6 + ( 3 + 0 ) + ( 5 + 4 ) = 18
( D2 ) = (1 + 8 ) + ( 3 + 0 ) + ( 4 + 2 ) = 18
7
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14
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21
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28
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35
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42
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49
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56
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63
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5.7. Tabla del siete.
( V ) = 14 + 35 + 56 = 105
( H ) = 28 + 35 + 42 = 105
( D1 ) = 7 + 35 + 63 = 105
( D2 ) = 21 + 35 + 49 = 105
( V ) = (1 + 4 ) + ( 3 + 5 ) + ( 5 + 6 ) = 24
( H ) = (2 + 8 ) + ( 3 + 5 ) + ( 4 + 2 ) = 24
( D1 ) = 7 + ( 3 + 5 ) + ( 6 + 3 ) = 24
( D2 ) = (2 + 1 ) + ( 3 + 5 ) + ( 4 + 9 ) = 24
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16
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24
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32
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40
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48
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56
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64
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72
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5.8. Tabla del ocho.
( V ) = 16 + 40 + 64 = 120
( H ) = 32 + 40 + 48 = 120
( D1 ) = 8 + 40 + 72 = 120
( D2 ) = 24 + 40 + 56 = 120
( V ) = (1 + 6 ) + ( 4 + 0 ) + ( 6 + 4 ) = 21
( H ) = (3 + 2 ) + ( 4 + 0 ) + ( 4 + 8 ) = 21
( D1 ) = 8 + ( 4 + 0 ) + ( 7 + 2 ) = 21
( D2 ) = (2 + 4 ) + ( 4 + 0 ) + ( 5 + 6 ) = 21
9
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18
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27
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36
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45
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54
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63
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72
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81
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5.9. Tabla del nueve
( V ) = 18 + 45 + 72 = 135
( H ) = 36 + 45 + 54 = 135
( D1 ) = 9 + 45 + 81 = 135
( D2 ) = 27 + 45 + 63 = 135
( V ) = (1 + 8 ) + ( 4 + 5 ) + ( 7 + 2 ) = 27
( H ) = (3 + 6 ) + ( 4 + 5 ) + ( 5 + 4 ) = 27
( D1 ) = 9 + ( 4 + 5 ) + ( 8 + 1 ) = 27
( D2 ) = (2 + 7 ) + ( 4 + 5 ) + ( 6 + 3 ) = 27
Ahora bien,si tomamos las tablas de multiplicar incluyendo la del uno ( siendo esta en la posición superior izquierda ) hasta la del nueve ( siendo esta en la posición inferior derecha ) en una tabla de 9 x 9 obtendremos los siguientes resultados :
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2
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3
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2
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4
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6
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3
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6
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9
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4
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5
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6
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8
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10
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12
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12
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15
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18
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7
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8
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9
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14
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16
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18
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21
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24
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27
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4
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8
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12
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5
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15
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6
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12
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18
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24
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20
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25
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30
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24
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30
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36
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28
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32
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36
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35
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40
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45
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42
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48
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54
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7
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14
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21
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8
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16
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24
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9
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18
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27
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28
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35
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42
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32
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40
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48
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36
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45
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54
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49
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56
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63
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56
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64
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72
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63
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72
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81
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5.10.1. Matriz general 9 x 9.
( V ) = 4 + 10 + 16 + 10 + 25 + 40 + 16 + 40 + 64 = 225
( H ) = 16 + 20 + 24 + 20 + 25 + 30 + 24 + 30 + 36 = 225
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12
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18
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9
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27
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30
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36
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28
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32
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36
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35
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45
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42
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48
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54
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7
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14
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21
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8
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16
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24
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9
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18
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27
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28
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35
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42
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32
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40
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48
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36
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45
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54
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49
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56
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63
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56
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64
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72
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63
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72
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81
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( D1 ) = 1 + 5 + 9 + 5 + 25 + 45 + 9 + 45 + 81 = 225
( D2 ) = 9 + 15 + 21 + 15 + 25 + 35 + 21 + 35 + 49 = 225
NOTA :
De cierto se puede decir que la multiplicación de un numero común cualesquiera por los números naturales dispuestos en un orden concreto, es una forma de obtener matrices místicas.
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