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这是一个创建于 2242 天前的主题，其中的信息可能已经有所发展或是发生改变。
九九表至少存在了三千多年，中国早在春秋战国时代就开始使用“九九口诀”在筹算中运算。在《荀子》、《管子》、《淮南子》、《战国策》等书中就能找到“三九二十七”、“六八四十八”、“四八三十二”、“六六三十六”等句子。由此可见，早在“春秋”、“战国”的时候，《九九乘法歌诀》就已经开始流行了。后来东传入高丽、日本，经过丝绸之路西传印度、波斯，继而流行全世界，到明代则改良并用在算盘上。十进位制和九九表是古代中国对世界文化的一项重要的贡献。现在，九九表也是小学算术的基本功
A × B：A 是被乘数，B 是乘数
以下是用 Python 程序生成“九九乘法表”的小例子
for b in range(1, 10): # 乘数；同一行被乘数不变
for a in range(1, 10): # 被乘数；同一行乘数逐渐递增，直到与被乘数相等
if a <= b: # 被乘数不能大于乘数（只是针对这个乘法表）
print(f'{a} X {b} = {a * b}'.ljust(11), end='\t')
print() # 换行
以上生成了 45 项积
古玛雅人用 20 进位制，跟现代世界通用的十进位制最接近。一个乘法表有 190 项，比九九表的 45 项虽然大三倍多，但比巴比伦方法还是简便得多。可是考古学家至今还没有发现任何玛雅乘法表。
以下代码生成了 20 进制的乘法表（只是将 10 改为 20，没有进行进制转换）
>>> for b in range(1, 20): # 乘数；同一行被乘数不变
... for a in range(1, 20): # 被乘数；同一行乘数逐渐递增，直到与被乘数相等
... if a <= b: # 被乘数不能大于乘数（只是针对这个乘法表）
... print(f'{a} X {b} = {a * b}', end='\t')
... print() # 换行
...
1 X 1 = 1
1 X 2 = 2 2 X 2 = 4
1 X 3 = 3 2 X 3 = 6 3 X 3 = 9
1 X 4 = 4 2 X 4 = 8 3 X 4 = 12 4 X 4 = 16
1 X 5 = 5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
1 X 6 = 6 2 X 6 = 12 3 X 6 = 18 4 X 6 = 24 5 X 6 = 30 6 X 6 = 36
1 X 7 = 7 2 X 7 = 14 3 X 7 = 21 4 X 7 = 28 5 X 7 = 35 6 X 7 = 42 7 X 7 = 49
1 X 8 = 8 2 X 8 = 16 3 X 8 = 24 4 X 8 = 32 5 X 8 = 40 6 X 8 = 48 7 X 8 = 56 8 X 8 = 64
1 X 9 = 9 2 X 9 = 18 3 X 9 = 27 4 X 9 = 36 5 X 9 = 45 6 X 9 = 54 7 X 9 = 63 8 X 9 = 72 9 X 9 = 81
1 X 10 = 10 2 X 10 = 20 3 X 10 = 30 4 X 10 = 40 5 X 10 = 50 6 X 10 = 60 7 X 10 = 70 8 X 10 = 80 9 X 10 = 90 10 X 10 = 100
1 X 11 = 11 2 X 11 = 22 3 X 11 = 33 4 X 11 = 44 5 X 11 = 55 6 X 11 = 66 7 X 11 = 77 8 X 11 = 88 9 X 11 = 99 10 X 11 = 110 11 X 11 = 121
1 X 12 = 12 2 X 12 = 24 3 X 12 = 36 4 X 12 = 48 5 X 12 = 60 6 X 12 = 72 7 X 12 = 84 8 X 12 = 96 9 X 12 = 108 10 X 12 = 120 11 X 12 = 132 12 X 12 = 144
1 X 13 = 13 2 X 13 = 26 3 X 13 = 39 4 X 13 = 52 5 X 13 = 65 6 X 13 = 78 7 X 13 = 91 8 X 13 = 104 9 X 13 = 117 10 X 13 = 130 11 X 13 = 143 12 X 13 = 156 13 X 13 = 169
1 X 14 = 14 2 X 14 = 28 3 X 14 = 42 4 X 14 = 56 5 X 14 = 70 6 X 14 = 84 7 X 14 = 98 8 X 14 = 112 9 X 14 = 126 10 X 14 = 140 11 X 14 = 154 12 X 14 = 168 13 X 14 = 182 14 X 14 = 196
1 X 15 = 15 2 X 15 = 30 3 X 15 = 45 4 X 15 = 60 5 X 15 = 75 6 X 15 = 90 7 X 15 = 105 8 X 15 = 120 9 X 15 = 135 10 X 15 = 150 11 X 15 = 165 12 X 15 = 180 13 X 15 = 195 14 X 15 = 210 15 X 15 = 225
1 X 16 = 16 2 X 16 = 32 3 X 16 = 48 4 X 16 = 64 5 X 16 = 80 6 X 16 = 96 7 X 16 = 112 8 X 16 = 128 9 X 16 = 144 10 X 16 = 160 11 X 16 = 176 12 X 16 = 192 13 X 16 = 208 14 X 16 = 224 15 X 16 = 240 16 X 16 = 256
1 X 17 = 17 2 X 17 = 34 3 X 17 = 51 4 X 17 = 68 5 X 17 = 85 6 X 17 = 102 7 X 17 = 119 8 X 17 = 136 9 X 17 = 153 10 X 17 = 170 11 X 17 = 187 12 X 17 = 204 13 X 17 = 221 14 X 17 = 238 15 X 17 = 255 16 X 17 = 272 17 X 17 = 289
1 X 18 = 18 2 X 18 = 36 3 X 18 = 54 4 X 18 = 72 5 X 18 = 90 6 X 18 = 108 7 X 18 = 126 8 X 18 = 144 9 X 18 = 162 10 X 18 = 180 11 X 18 = 198 12 X 18 = 216 13 X 18 = 234 14 X 18 = 252 15 X 18 = 270 16 X 18 = 288 17 X 18 = 306 18 X 18 = 324
1 X 19 = 19 2 X 19 = 38 3 X 19 = 57 4 X 19 = 76 5 X 19 = 95 6 X 19 = 114 7 X 19 = 133 8 X 19 = 152 9 X 19 = 171 10 X 19 = 190 11 X 19 = 209 12 X 19 = 228 13 X 19 = 247 14 X 19 = 266 15 X 19 = 285 16 X 19 = 304 17 X 19 = 323 18 X 19 = 342 19 X 19 = 361
以下代码生成的是进行进制转换的 20 进制 JJ 乘法表
>>> from numpy import base_repr
>>> for b in range(1, 20): # 乘数；同一行被乘数不变
... for a in range(1, 20): # 被乘数；同一行乘数逐渐递增，直到与被乘数相等
... if a <= b: # 被乘数不能大于乘数（只是针对这个乘法表）
... print(f'{base_repr(a, 20)} X {base_repr(b, 20)} = {base_repr(a * b, 20)}', end='\t')
... print() # 换行
...
1 X 1 = 1
1 X 2 = 2 2 X 2 = 4
1 X 3 = 3 2 X 3 = 6 3 X 3 = 9
1 X 4 = 4 2 X 4 = 8 3 X 4 = C 4 X 4 = G
1 X 5 = 5 2 X 5 = A 3 X 5 = F 4 X 5 = 10 5 X 5 = 15
1 X 6 = 6 2 X 6 = C 3 X 6 = I 4 X 6 = 14 5 X 6 = 1A 6 X 6 = 1G
1 X 7 = 7 2 X 7 = E 3 X 7 = 11 4 X 7 = 18 5 X 7 = 1F 6 X 7 = 22 7 X 7 = 29
1 X 8 = 8 2 X 8 = G 3 X 8 = 14 4 X 8 = 1C 5 X 8 = 20 6 X 8 = 28 7 X 8 = 2G 8 X 8 = 34
1 X 9 = 9 2 X 9 = I 3 X 9 = 17 4 X 9 = 1G 5 X 9 = 25 6 X 9 = 2E 7 X 9 = 33 8 X 9 = 3C 9 X 9 = 41
1 X A = A 2 X A = 10 3 X A = 1A 4 X A = 20 5 X A = 2A 6 X A = 30 7 X A = 3A 8 X A = 40 9 X A = 4A A X A = 50
1 X B = B 2 X B = 12 3 X B = 1D 4 X B = 24 5 X B = 2F 6 X B = 36 7 X B = 3H 8 X B = 48 9 X B = 4J A X B = 5A B X B = 61
1 X C = C 2 X C = 14 3 X C = 1G 4 X C = 28 5 X C = 30 6 X C = 3C 7 X C = 44 8 X C = 4G 9 X C = 58 A X C = 60 B X C = 6C C X C = 74
1 X D = D 2 X D = 16 3 X D = 1J 4 X D = 2C 5 X D = 35 6 X D = 3I 7 X D = 4B 8 X D = 54 9 X D = 5H A X D = 6A B X D = 73 C X D = 7G D X D = 89
1 X E = E 2 X E = 18 3 X E = 22 4 X E = 2G 5 X E = 3A 6 X E = 44 7 X E = 4I 8 X E = 5C 9 X E = 66 A X E = 70 B X E = 7E C X E = 88 D X E = 92 E X E = 9G
1 X F = F 2 X F = 1A 3 X F = 25 4 X F = 30 5 X F = 3F 6 X F = 4A 7 X F = 55 8 X F = 60 9 X F = 6F A X F = 7A B X F = 85 C X F = 90 D X F = 9F E X F = AA F X F = B5
1 X G = G 2 X G = 1C 3 X G = 28 4 X G = 34 5 X G = 40 6 X G = 4G 7 X G = 5C 8 X G = 68 9 X G = 74 A X G = 80 B X G = 8G C X G = 9C D X G = A8 E X G = B4 F X G = C0 G X G = CG
1 X H = H 2 X H = 1E 3 X H = 2B 4 X H = 38 5 X H = 45 6 X H = 52 7 X H = 5J 8 X H = 6G 9 X H = 7D A X H = 8A B X H = 97 C X H = A4 D X H = B1 E X H = BI F X H = CF G X H = DC H X H = E9
1 X I = I 2 X I = 1G 3 X I = 2E 4 X I = 3C 5 X I = 4A 6 X I = 58 7 X I = 66 8 X I = 74 9 X I = 82 A X I = 90 B X I = 9I C X I = AG D X I = BE E X I = CC F X I = DA G X I = E8 H X I = F6 I X I = G4
1 X J = J 2 X J = 1I 3 X J = 2H 4 X J = 3G 5 X J = 4F 6 X J = 5E 7 X J = 6D 8 X J = 7C 9 X J = 8B A X J = 9A B X J = A9 C X J = B8 D X J = C7 E X J = D6 F X J = E5 G X J = F4 H X J = G3 I X J = H2 J X J = I1
巴比伦算术有进位制，比希腊等几个国家有很大的进步。不过巴比伦算术采用 60 进位制，原则上一个“ 59×59 ”乘法表需要 1770 项；由于“ 59×59 ”乘法表太庞大，巴比伦人从来不用类似于九九表的“乘法表”。考古学家也从来没有发现类似于九九表的“ 59×59 ”乘法表。不过，考古学家发现巴比伦人用独特的是“平方表”：1×1=1，2×2=4，3×3=9，...，59×59=3481，巴比伦人则依靠他们最擅长的代数学来计算两个数a、b的乘积：
例如：
现代的九九表只需 45 项，玛雅乘法表需 190 项，巴比伦乘法表须 1770 项，埃及、希腊、罗马、印度等国的乘法表须无穷多项；
参考资料：
https://baike.baidu.com/item/九九乘法口诀表 /10467766
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junjieyuanxiling 2018-11-07 21:52:37 +08:00 via Android
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CEBBCAT 2018-11-07 23:56:25 +08:00
楼主你再这样可能招致不少人包括我的屏蔽……
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不要浪费论坛资源。
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glaucus 2018-11-12 08:53:22 +08:00
？你在干嘛？
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