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1             3000                                                                                                1




                     1




                                                                                                                           3000
                                                                                                                           3000
                         (Writing Numbers)


                         (place value system)




                                                                                                       365
                                                                5   5   6   60                 3   300

                                        3000
                                                                                                   1         10
                              365




                                                                        3 602 21 60 43 12103

                                                Three hundred
     and sixty-five                                      365




          3    100   6   10         5

              3 100 6 10 5



                                                       0   9
     10

10                                                                                                                    11
2            3000                                                                                                        2




                                 2




                                                                                                                                  3000
                                                                                                                                  3000
                                         (Fractions)




                                                                                              5   8          5/8 0.625



            2/3                                                           1                           p.10

                     (aliquot fraction)             1/2 1/3 1/4


     2/5            1/5    1/5                    1/5                          1/5
              1/6   1/30                      2/5       2/5   1/5   1/6       1/30




                     1650
                                                                                   60
                           (minute parts)                                     60
                  (second minute parts)
                                                               60
     60
                                             60


              1/2 1/3 1/4            1/9                                                4
           (1/2 1/4 1/5 1/8)                        4 (1/3 1/6 1/7 1/9)
                  1/3 0.3333         3                                                  1/7

12                                                                                                                           13
3                2000                                                                                                 3




                        3




                                                                                                                               3000
                                                                                                                               3000
                             (Quadratic Equations)




                 quadratus         quadratic


                                                                                                0.75   x2 + x = 0.75
                                                                       1                               x          1
                                                           1                  0.5                      1          0.5
          2
     ax       bx c 0                                       0.5       0.5      0.25                            2
                                                                                                       (0.5) = 0.25
                                                           0.25        0.75     1                      0.25 + 0.75 = 1
              a b c                                            1                                           1 =1
                                                     X               0.5                               1- 0.5 = 0.5
                                                         0.5                                           x = 0.5


                                                                                     ax2 + bx = c




                                                               a=1



                                 0.75



14                                                                                                                        15
4             1850                                                                                      4




                       4

                            (The Greatest Pyramid)




                                                                                                                 3000
                                                                                                                 3000
                             (frustum of a pyramid)




                                                                                    h           r
                                                        R
                                                      (1/3) h ( R2+ Rr+ r 2 )

                                                                                            r
                                                                         2
                                       1850




                                  6                                             6                   h

                        4                     2
     4         16
     4    2 8
     2         4                                                         4
                                                                                        R
     16 8       4      28
     6    3        2
     2    28 56




     (1/3) x 6 (42+2x4+22) = 56




16                                                                                                          17
5                                                                                                     5




                     5




                                                                                                           3000
                                                                腦。)   70                   2037




                                                       p



     4x(8/9) 2       3.16          3.14                23
                 3


                                                  96                       ENIAC p.190   pp.101-102
            223/71 22/7
                         (429-501)               355/113


       (Madhava)


         /4 = 1- 1/3+ 1/5 - 1/7+



                            11



                     1949        ENIAC(譯註:電子數值積分電腦(Electronic
     Numerical Integrator and Computer),是世界上第一部可變程式的電

18                                                                                                    19
6                                                                                      7




     6                                                       7


         (The Pythagoreans)                                      (Pythagoras s Theorem)




                                                                                                                    600
                                                                                                                    150
                                                             a b c
                                          c                             4                      b

                                                                            a+b            a
                                                                                                   c
                                                      4




                                                  c                    c2                                  a
                                                                                                       c
                                                                                               b
                              (reality)
                                              a                  b           a2 + b2


                                              c2 = a2 + b2




20                                                                                                             21

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版型0118

  • 1. 1 3000 1 1 3000 3000 (Writing Numbers) (place value system) 365 5 5 6 60 3 300 3000 1 10 365 3 602 21 60 43 12103 Three hundred and sixty-five 365 3 100 6 10 5 3 100 6 10 5 0 9 10 10 11
  • 2. 2 3000 2 2 3000 3000 (Fractions) 5 8 5/8 0.625 2/3 1 p.10 (aliquot fraction) 1/2 1/3 1/4 2/5 1/5 1/5 1/5 1/5 1/6 1/30 2/5 2/5 1/5 1/6 1/30 1650 60 (minute parts) 60 (second minute parts) 60 60 60 1/2 1/3 1/4 1/9 4 (1/2 1/4 1/5 1/8) 4 (1/3 1/6 1/7 1/9) 1/3 0.3333 3 1/7 12 13
  • 3. 3 2000 3 3 3000 3000 (Quadratic Equations) quadratus quadratic 0.75 x2 + x = 0.75 1 x 1 1 0.5 1 0.5 2 ax bx c 0 0.5 0.5 0.25 2 (0.5) = 0.25 0.25 0.75 1 0.25 + 0.75 = 1 a b c 1 1 =1 X 0.5 1- 0.5 = 0.5 0.5 x = 0.5 ax2 + bx = c a=1 0.75 14 15
  • 4. 4 1850 4 4 (The Greatest Pyramid) 3000 3000 (frustum of a pyramid) h r R (1/3) h ( R2+ Rr+ r 2 ) r 2 1850 6 6 h 4 2 4 16 4 2 8 2 4 4 R 16 8 4 28 6 3 2 2 28 56 (1/3) x 6 (42+2x4+22) = 56 16 17
  • 5. 5 5 5 3000 腦。) 70 2037 p 4x(8/9) 2 3.16 3.14 23 3 96 ENIAC p.190 pp.101-102 223/71 22/7 (429-501) 355/113 (Madhava) /4 = 1- 1/3+ 1/5 - 1/7+ 11 1949 ENIAC(譯註:電子數值積分電腦(Electronic Numerical Integrator and Computer),是世界上第一部可變程式的電 18 19
  • 6. 6 7 6 7 (The Pythagoreans) (Pythagoras s Theorem) 600 150 a b c c 4 b a+b a c 4 c c2 a c b (reality) a b a2 + b2 c2 = a2 + b2 20 21