Bản Giao Hưởng Toán Học
Cùng xem và tìm hiểu về những cái hay của các con số, nhịp nhàng, êm dịu như một bản giao hưởng đầy âm sắt
The Number Symphonies of Royal Heath: Symphony no. 1
09 = 32
1089 = 332
110889 = 3332
111088889 = 33332
11110888889 = 333332
16 = 42
1156 = 342
111556 = 3342
11115556 = 33342
1111155556 = 333342
49 = 72
4489 = 672
444889 = 6672
44448889 = 66672
4444488889 = 666672
81 = 92
9801 = 992
998001 = 9992
99980001 = 99992
9999800001 = 999992
1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321
11111 × 11111 = 123454321
111111 × 111111 = 12345654321
1111111 × 1111111 = 1234567654321
11111111 × 11111111 = 123456787654321
111111111 × 111111111 = 12345678987654321
1 + 1 + 1 = 3 3 × 37 = 111
2 + 2 + 2 = 6 6 × 37 = 222
3 + 3 + 3 = 9 9 × 37 = 333
4 + 4 + 4 = 12 12 × 37 = 444
5 + 5 + 5 = 15 15 × 37 = 555
6 + 6 + 6 = 18 18 × 37 = 666
7 + 7 + 7 = 21 21 × 37 = 777
8 + 8 + 8 = 24 24 × 37 = 888
9 + 9 + 9 = 27 27 × 37 = 999
1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = 111111
123456 × 9 + 7 = 1111111
1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111
123456789 × 9 + 10 = 1111111111
1 × 8 + 1 = 9 9 × 9 + 7 = 88
12 × 8 + 2 = 98 9 × 98 + 6 = 888
123 × 8 + 3 = 987 9 × 987 + 5 = 8888
1234 × 8 + 4 = 9876 9 × 9876 + 4 = 88888
12345 × 8 + 5 = 98765 9 × 98765 + 3 = 888888
123456 × 8 + 6 = 987654 9 × 987654 + 2 = 8888888
1234567 × 8 + 7 = 9876543 9 × 9876543 + 1 = 88888888
12345678 × 8 + 8 = 98765432 9 × 98765432 + 0 = 888888888
123456789 × 8 + 9 = 987654321 9 × 987654321 − 1 = 8888888888
(1)2 = 13
(1 + 2)2 = 13 + 23
(1 + 2 + 3)2 = 13 + 23 + 33
(1 + 2 + 3 + 4)2 = 13 + 23 + 33 + 43
(1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53
(1 + 2 + 3 + 4 + 5 + 6)2 = 13 + 23 + 33 + 43 + 53 + 63
(1 + 2 + 3 + 4 + 5 + 6 + 7)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 )2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93 + 103
19 × 1 = 19 1 + 9 = 10 1 + 0 = 1 1089 × 1 = 1089 1 + 0 + 8 + 9 = 18
19 × 2 = 38 3 + 8 = 11 1 + 1 = 2 1089 × 2 = 2178 2 + 1 + 7 + 8 = 18
19 × 3 = 57 5 + 7 = 12 1 + 2 = 3 1089 × 3 = 3267 3 + 2 + 6 + 7 = 18
19 × 4 = 76 7 + 6 = 13 1 + 3 = 4 1089 × 4 = 4356 4 + 3 + 5 + 6 = 18
19 × 5 = 95 9 + 5 = 14 1 + 4 = 5 1089 × 5 = 5445 5 + 4 + 4 + 5 = 18
19 × 6 = 114 11 + 4 = 15 1 + 5 = 6 1089 × 6 = 6534 6 + 5 + 3 + 4 = 18
19 × 7 = 133 13 + 3 = 16 1 + 6 = 7 1089 × 7 = 7623 7 + 6 + 2 + 3 = 18
19 × 8 = 152 15 + 2 = 17 1 + 7 = 8 1089 × 8 = 8712 8 + 7 + 1 + 2 = 18
19 × 9 = 171 17 + 1 = 18 1 + 8 = 9 1089 × 9 = 9801 9 + 8 + 0 + 1 = 18
19 × 10 = 190 19 + 0 = 19 1 + 9 = 10 1089 × 10 = 10890 1 + 0 + 8 + 9 + 0 = 18
1089 = 332
110889 = 3332
111088889 = 33332
11110888889 = 333332
16 = 42
1156 = 342
111556 = 3342
11115556 = 33342
1111155556 = 333342
49 = 72
4489 = 672
444889 = 6672
44448889 = 66672
4444488889 = 666672
81 = 92
9801 = 992
998001 = 9992
99980001 = 99992
9999800001 = 999992
1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321
11111 × 11111 = 123454321
111111 × 111111 = 12345654321
1111111 × 1111111 = 1234567654321
11111111 × 11111111 = 123456787654321
111111111 × 111111111 = 12345678987654321
1 + 1 + 1 = 3 3 × 37 = 111
2 + 2 + 2 = 6 6 × 37 = 222
3 + 3 + 3 = 9 9 × 37 = 333
4 + 4 + 4 = 12 12 × 37 = 444
5 + 5 + 5 = 15 15 × 37 = 555
6 + 6 + 6 = 18 18 × 37 = 666
7 + 7 + 7 = 21 21 × 37 = 777
8 + 8 + 8 = 24 24 × 37 = 888
9 + 9 + 9 = 27 27 × 37 = 999
1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = 111111
123456 × 9 + 7 = 1111111
1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111
123456789 × 9 + 10 = 1111111111
1 × 8 + 1 = 9 9 × 9 + 7 = 88
12 × 8 + 2 = 98 9 × 98 + 6 = 888
123 × 8 + 3 = 987 9 × 987 + 5 = 8888
1234 × 8 + 4 = 9876 9 × 9876 + 4 = 88888
12345 × 8 + 5 = 98765 9 × 98765 + 3 = 888888
123456 × 8 + 6 = 987654 9 × 987654 + 2 = 8888888
1234567 × 8 + 7 = 9876543 9 × 9876543 + 1 = 88888888
12345678 × 8 + 8 = 98765432 9 × 98765432 + 0 = 888888888
123456789 × 8 + 9 = 987654321 9 × 987654321 − 1 = 8888888888
(1)2 = 13
(1 + 2)2 = 13 + 23
(1 + 2 + 3)2 = 13 + 23 + 33
(1 + 2 + 3 + 4)2 = 13 + 23 + 33 + 43
(1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53
(1 + 2 + 3 + 4 + 5 + 6)2 = 13 + 23 + 33 + 43 + 53 + 63
(1 + 2 + 3 + 4 + 5 + 6 + 7)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 )2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93 + 103
19 × 1 = 19 1 + 9 = 10 1 + 0 = 1 1089 × 1 = 1089 1 + 0 + 8 + 9 = 18
19 × 2 = 38 3 + 8 = 11 1 + 1 = 2 1089 × 2 = 2178 2 + 1 + 7 + 8 = 18
19 × 3 = 57 5 + 7 = 12 1 + 2 = 3 1089 × 3 = 3267 3 + 2 + 6 + 7 = 18
19 × 4 = 76 7 + 6 = 13 1 + 3 = 4 1089 × 4 = 4356 4 + 3 + 5 + 6 = 18
19 × 5 = 95 9 + 5 = 14 1 + 4 = 5 1089 × 5 = 5445 5 + 4 + 4 + 5 = 18
19 × 6 = 114 11 + 4 = 15 1 + 5 = 6 1089 × 6 = 6534 6 + 5 + 3 + 4 = 18
19 × 7 = 133 13 + 3 = 16 1 + 6 = 7 1089 × 7 = 7623 7 + 6 + 2 + 3 = 18
19 × 8 = 152 15 + 2 = 17 1 + 7 = 8 1089 × 8 = 8712 8 + 7 + 1 + 2 = 18
19 × 9 = 171 17 + 1 = 18 1 + 8 = 9 1089 × 9 = 9801 9 + 8 + 0 + 1 = 18
19 × 10 = 190 19 + 0 = 19 1 + 9 = 10 1089 × 10 = 10890 1 + 0 + 8 + 9 + 0 = 18
The Number Symphonies of Royal Heath: Symphony no. 2
1/7 = .142857
142857 × 1 = 142857 142857 × 7 = 999999 999999 ÷ 9 = 111111
142857 × 3 = 428571 428571 × 7 = 2999997 2999997 ÷ 9 = 333333
142857 × 2 = 285714 285714 × 7 = 1999998 1999998 ÷ 9 = 222222
142857 × 6 = 857142 857142 × 7 = 5999994 5999994 ÷ 9 = 666666
142857 × 4 = 571428 571428 × 7 = 3999996 3999996 ÷ 9 = 444444
142857 × 5 = 714285 714285 × 7 = 4999995 4999995 ÷ 9 = 555555
142857 × 3 = 428571 428571 × 7 = 2999997 2999997 ÷ 9 = 333333
142857 × 2 = 285714 285714 × 7 = 1999998 1999998 ÷ 9 = 222222
142857 × 6 = 857142 857142 × 7 = 5999994 5999994 ÷ 9 = 666666
142857 × 4 = 571428 571428 × 7 = 3999996 3999996 ÷ 9 = 444444
142857 × 5 = 714285 714285 × 7 = 4999995 4999995 ÷ 9 = 555555
The Number Symphonies of Royal Heath: Symphony no. 3
1 + 2 = 3
4 + 5 + 6 = 7 + 8
9 + 10 + 11 + 12 = 13 + 14 + 15
16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
25 + 26 + 27 + 28 + 29 + 30 = 31 + 32 + 33 + 34 + 35
36 + 37 + 38 + 39 + 40 + 41 + 42 = 43 + 44 + 45 + 46 + 47 + 48
49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 = 57 + 58 + 59 + 60 + 61 + 62 + 63
64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 = 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80
81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 = 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99
4 + 5 + 6 = 7 + 8
9 + 10 + 11 + 12 = 13 + 14 + 15
16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
25 + 26 + 27 + 28 + 29 + 30 = 31 + 32 + 33 + 34 + 35
36 + 37 + 38 + 39 + 40 + 41 + 42 = 43 + 44 + 45 + 46 + 47 + 48
49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 = 57 + 58 + 59 + 60 + 61 + 62 + 63
64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 = 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80
81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 = 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99
1. In any line, the number of terms to the left of the equal sign is one more than the number of terms to the right of the equal sign. The product of these two numbers is the middle term of the line.
2. The difference between any term and the one immediately below it is always equal between any two lines, and the difference increases by 2 from line to line.
3. The first term of every line is a perfect square.
2. The difference between any term and the one immediately below it is always equal between any two lines, and the difference increases by 2 from line to line.
3. The first term of every line is a perfect square.
The Number Symphonies of Royal Heath: Symphony no. 4
32 + 42 = 52
102 + 112 + 122 = 132 + 142
212 + 222 + 232 + 242 = 252 + 262 + 272
362 + 372 + 382 + 392 + 402 = 412 + 422 + 432 + 442
552 + 562 + 572 + 582 + 592 + 602 = 612 + 622 + 632 + 642 + 652
782 + 792 + 802 + 812 + 822 + 832 + 842 = 852 + 862 + 872 + 882 + 892 + 902
102 + 112 + 122 = 132 + 142
212 + 222 + 232 + 242 = 252 + 262 + 272
362 + 372 + 382 + 392 + 402 = 412 + 422 + 432 + 442
552 + 562 + 572 + 582 + 592 + 602 = 612 + 622 + 632 + 642 + 652
782 + 792 + 802 + 812 + 822 + 832 + 842 = 852 + 862 + 872 + 882 + 892 + 902
1. In any line, the number of terms to the left of the equal sign is one more than the number of terms to the right of the equal sign. The product of these two numbers is half the middle term of the line.
2. From the last term of a line to the first term of the next line, there is, instead of an increase by 1, an increase by an odd integer which itself increases by 2 from line to line.
2. From the last term of a line to the first term of the next line, there is, instead of an increase by 1, an increase by an odd integer which itself increases by 2 from line to line.
God made man. Man made maths. Maths makes man mad.
Sưu Tầm
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