盤算數學 (11)
代數原本,應用延伸。
❶E = 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 ∴ E - 1 = A 倒數
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
數線上點數與間隔數 E≧2
E = A +1 , E點數,A間隔數
❹E = A 幾何圖形的代數式
E 頂點數 , A 邊數 , E≧3
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
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
等差數列的差數d,首數A,個數N
求末數E?
∵ N = (E - A) ÷d +1
∴ (N - 1) ×d +A = E
☆移項原理如同 : 一步一腳印
圖示 : 歸零 手撥珠,眼看,腦驗證
Computing Mathematics (11)
Algebraic original, application extension.
❶E = 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 ∴ E - 1 = A reciprocal
An almanac of an abacus
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
Number of points on the line and the number of intervals E ≧ 2
E = A +1, E points, A number of intervals
Algebraic representation of geometric figures
E vertex number, A side number, E ≧ 3
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 = big - small +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
The difference number d, the first number A, the number N of the difference series
The final number of E
∵ N = (E - A) ÷ d +1
∴ (N - 1) × d + A = E
☆ shift as the principle:
step by step footprints
Illustration: Zero hand dial, seeing, brain verification
