4 (1) okamotoy@uec.ac.jp 2014 5 13 2014 5 12 09:28 ( ) (4) 2014 5 13 1 / 35
() 1 (1) (4 8 ) 2 (2) (4 15 ) 3 (3) (4 22 ) () (4 29 ) () (5 6 ) 4 (1) (5 13 ) 5 (2) (5 20 ) 6 (4) (5 27 ) 7 (1) (6 3 ) (6 10 ) ( ) (4) 2014 5 13 2 / 35
() 8 (2) (6 17 ) () (6 24 ) () (7 1 ) 9 (1) (7 8 ) 10 (2) (7 15 ) 11 (3) (7 22 ) 12 (5) (7 29 ) 13 (3) (8 5 ) (8 12 ) ( ) (4) 2014 5 13 3 / 35
6 10 ( ) 6 A201 1 (4 8 ) 6 (5 27 ) 6 3 1 10 60 90 A4 1 ( ) min{100, + } ( ) (4) 2014 5 13 4 / 35
( ) 2 1 ( ) 2 ( ) (4) 2014 5 13 5 / 35
( ) () ( ) (4) 2014 5 13 6 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 7 / 35
( ) { } {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} {,,,, } 1 1 ( ) (4) 2014 5 13 8 / 35
x A x A x A x A A = {,,,, } A A A A ( ) (4) 2014 5 13 9 / 35
(1) U = {,,,,,,,,,,,,,,,,,,,,,,, } = ( ) (4) 2014 5 13 10 / 35
(2) U = {x x (2014 ) } {x x () } : ; ( ) (4) 2014 5 13 11 / 35
A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n 3 + 101n 2 247n + 210 = 0 () ( ) (4) 2014 5 13 12 / 35
A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n 3 + 101n 2 247n + 210 = 0 () ( ) (4) 2014 5 13 12 / 35
A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n 3 + 101n 2 247n + 210 = 0 () ( ) (4) 2014 5 13 12 / 35
A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n 3 + 101n 2 247n + 210 = 0 () ( ) (4) 2014 5 13 12 / 35
A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n 3 + 101n 2 247n + 210 = 0 () ( ) (4) 2014 5 13 12 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) 2014 5 13 13 / 35
() N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) 2014 5 13 14 / 35
() N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) 2014 5 13 14 / 35
() N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) 2014 5 13 14 / 35
() N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) 2014 5 13 14 / 35
() N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) 2014 5 13 14 / 35
{2, 3, 5, 7} 1 2 3 5 7 2 2 3 5 7 ( ) (4) 2014 5 13 15 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 16 / 35
A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {a, b, c} A d e f a b c g h B ( ) (4) 2014 5 13 17 / 35
A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {a, b, c, d, e, f, g, h} A d e f a b c g h B ( ) (4) 2014 5 13 18 / 35
A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {d, e, f } A d e f a b c g h B A BA \ B ( ) (4) 2014 5 13 19 / 35
1 { } 2 Φ φ ( ) (4) 2014 5 13 20 / 35
Constructive Solid Geometry Constructive Solid Geometry http://en.wikipedia.org/wiki/file:csg tree.png ( ) (4) 2014 5 13 21 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 22 / 35
2 A = {a, b, c, d, e, f } B = {a, b, c, d, e, f, g, h, i} A B A a b c d e f B g h i () A B A B () ( ) (4) 2014 5 13 23 / 35
( ) A B x A x B 2 A = {a, b, c, d, e, f } B = {a, b, c, d, e, f, g, h, i} A B A a b c d e f B g h i A B A B A B A B ( ) (4) 2014 5 13 24 / 35
N = Z = Q = R = C = N Z Z Q Q R R C ( ) (4) 2014 5 13 25 / 35
2 A B A B B A A = B B A A = B A and B ( ) (4) 2014 5 13 26 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 27 / 35
1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) 2014 5 13 28 / 35
1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) 2014 5 13 28 / 35
1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) 2014 5 13 28 / 35
1 ( ) 1 A = {1, 2, 3} B = {2, 3, 4} A B 1 A 1 B ( ) (4) 2014 5 13 29 / 35
2 2 A, B A B A B A, B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 30 / 35
2 2 A, B A B A B A, B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 30 / 35
2 2 A, B A B A B A, B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 30 / 35
2 2 A, B A B A B A, B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 30 / 35
2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 31 / 35
2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 31 / 35
2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B 1 1 2 () ( ) (4) 2014 5 13 31 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 32 / 35
( ) () ( ) (4) 2014 5 13 33 / 35
( ) OK OK ( ) (4) 2014 5 13 34 / 35
1 2 3 4 5 ( ) (4) 2014 5 13 35 / 35