2017年9月23日 星期六

原本即自然

 『原本相通究自然』
     E = A  +1  算式說故事
⑴數有原本
    整數一個一數,連續數 +1 即加法
     E : 後項    A : 前項
⑵代數原本
    算盤代數基本式
     E : 進位數 , A : 珠數 , A ≧ 1
⑶幾何原本
    二點成一線段
     E : 點數 , A : 線段數 , E ≧ 2
⑷標地數 = 間隔數  +1
     E : 標地數 , A : 間隔數
    直線非封閉排列代數式 E = A +1
    如數線上等距點數與間隔數
⑸幾何圖形的終點必回到起點
    頂點數等於邊數的封閉排列圖形
    E = A  幾何圖形代數式
    E : 頂點數  ,  A : 邊數  ,  E≧3
⑹∵ E =A +1 , E -1 =A , ∴ -1 =A -E
    倒數是依續 -1 即減法
⑺E  =  A  +1  ,  E後項 , A前項  
    0,1,2,3,4,5,6,7,8,9 ,,,
    整數一個一數
    連續整數的代數基本式
   ∵E = A +1連續數∴E - 1 = A 倒數
⑻一段算盤的代數式
    E  =  A  +1 , E進位數,A各檔珠數
    二段算盤, E進位數,AB各檔珠數
    E  =  (A+1)×(B+1)
    三段 , E進位值 , ABC各檔珠數
    E  =  (A+1)×(B+1)×(C+1)
    四段 , E進位數,ABCD各檔珠數
    E  =  (A+1)×(B+1)×(C+1)×(D+1)
   算盤  段數≧1, 檔數≧1, 珠數≧1
⑼連續整數自首A數至末E有N個
    A , A+1 , A+2 , A+3 , , , E
    E > A  ,    N =    E  - A         +1
               個數 = (大 - 小) ÷1 +1
    2 個一數自 A 數至 E 有N個
    A , A+2 , A+4 , A+6 , , , E
           N = (E - A) ÷2 +1
    3 個一數自 A 數至 E 有N個
    A , A+3 , A+6 , A+9 , , , E
           N = (E - A) ÷3 +1
    d 個一數自 A 數至 E 有N個
    A , A+d , A+2d , A+3d , , , E
           N = (E - A) ÷d +1
   等差數列的差數d,即 d 個一數
   個數 = (末數 - 首數) ÷差數 + 1
   末數 = (個數  - 1 ) ×差數 +首數
    ∵  N = (E - A) ÷d +1
    ∴ (N - 1) ×d +A = E
    移項原理如同 : 一步一腳印
    歸零 : 手撥珠,眼看,腦推證演
⑽三角形底邊異於兩端點,補上 N
    個點後,形成幾個不同的三角形?
    形成  1+2+3+…+(N+1)  個三角形
    總和=(N+1+1)×(N+1)÷2
            =(N+1)×(N+2)÷2
            =(N²+3N+2)÷2
☆『原本相通究自然』
    原本的數有,代數,幾何皆相通

"The original nature of nature"
     E = A + 1 formula
⑴ number of original
    Integer a number, continuous number +1 or addition
     E: Item A: The preceding paragraph
⑵ algebra original
    Abacus Algebra Basic
     E: carry, A: beads, A ≧ 1
⑶ geometric original
    Two points into a line
     E: number of points, A: number of lines, E ≧ 2
⑷ Landmark number = number of intervals +1
     E: Number of places, A: number of intervals
    Linear non - closed algebraic E = A +1
    Such as the number of equidistant points on the line and the number of intervals
⑸ the end of the geometry will return to the starting point
    A closed array of vertices equal to the number of edges
    E = A Geometric Algebra
    E: vertex number, A: edge number, E ≧ 3
⑹ ∵ E = A +1, E -1 = A, ∴ -1 = A -E
    The reciprocal is continued by -1 or subtraction
⑺E = A +1, E after the item, A before the item
    0,1,2,3,4,5,6,7,8,9 ,,,
    The integer is one by one
    The Algebraic Basic of Continuous Integer
   ∵E = A +1 continuous number ∴E - 1 = A reciprocal
⑻ an almanac of arithmetic
    E = A +1, E carry digits, A number of stalls
    Two abacus, E carry the number of, AB the number of stalls
    E = (A + 1) × (B + 1)
    Three paragraphs, E carry value, ABC file number of beads
    E = (A + 1) × (B + 1) × (C + 1)
    Four, E carry the number of ABCD file number
    E = (A + 1) × (B + 1) × (C + 1) × (D + 1)
   Abacus number ≧ 1, the number of stalls ≧ 1, beads ≧ 1
⑼ continuous integer surrendered A number to the end of E have N
    A, A + 1, A + 2, A + 3,,, E
    E> A, N = E - A +1
               Number = (large - small) ÷ 1 +1
    2 number from A number to E have N number
    A, A + 2, A + 4, A + 6,,, E
           N = (E - A) ÷ 2 +1
    3 number from A number to E have N number
    A, A + 3, A + 6, A + 9,
           N = (E - A) ÷ 3 + 1
    D number from A number to E have N number
    A, A + d, A + 2d, A + 3d,
           N = (E - A) ÷ d +1
   The difference d of the difference series is the number of d
   Number = (the last number - the first number) ÷ difference + 1
   The last number = (number - 1) × difference number + first number
    ∵ N = (E - A) ÷ d +1
    ∴ (N - 1) × d + A = E
    Shift the principle as follows: step by step
    Return to zero: hand dial beads, seeing, brain push show
⑽ triangular bottom edge is different from the two ends, make up N
    After a few points, form a few different triangles
    Form 1 + 2 + 3 + ... + (N + 1) triangles
    Sum = (N + 1 + 1) × (N + 1) ÷ 2
            = (N + 1) × (N + 2) ÷ 2
            = (N² + 3N + 2) ÷ 2
☆ "the original nature of nature"
    The original number of algebra, geometry are interlinked

沒有留言:

張貼留言