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
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