2.數學軟體Geogebra(ggb)輔助學習與應用
ex1. 2,4,8,... ,a10,....,an
a1=2
r=4/2=2
a10=a1*r^9=2*2^9=2^10=1024
an=a1*r^(n-1)=2^(n-1)
ggb code
n=Slider(1,10,1)
a1=2
r=2
a10=a1*r^9
l1=Sequence(a1*r^(i-1),i,1,10) #a1=a1*r^0, a10=a1*r^9 #第一個產生的list , Geogebra default l1
Sequence(a1*r^i,i,0,9) #a1=a1*r^0, a10=a1*r^9 #也可以這樣寫法
l1(10) #a10
sum(l1)
a1(1-r^10)/(1-r) # 結果與sum(l1) 相同
ex2. 3,9,27,...
a1=3
r=3
a10=a1*r^9
Sequence(a1*r^(i-1),i,1,10)
l1(10) #a10
a1(1-r^10)/(1-r)
sum(l1)
2021/6/18 光的反射
Geogebra App
eq1:x=0 # y axis ,法線, red, 虛線
y=0 #x axis , 鏡面, blue
A=(3,4)
Segment(A,O) #線段
A'=Reflect(A,eq1) #反射
Ray(O,A') #射線
h=Polyline(A,O,A')
C=Point(h)
StartAnimation(C)
檔名:20210618光的反射-班級 座號 姓名
Geogebra 組合指令
BinomialCoefficient( <Number>, <Number> )
或
nCr( <Number>, <Number> )
Calculates the binomial coefficient .
The first Number represents all elements n and the second Number represents the selected elements r.
BinomialCoefficient(10,1) yields 10
nCr(10,1)
BinomialCoefficient(10,2) yields 10*9 /(2*1)
nCr(10,2)
BinomialCoefficient(10,3) yields 10*9 *8/(3*2*1)
nCr(10,3)
BinomialCoefficient(10,8) yields 45
nCr(10,8)
BinomialCoefficient(10,9) yields 10
nCr(10,9)
數學上 C(n,r)=C(n,n-r)
由上面數值實驗可知
BinomialCoefficient(10,1) = BinomialCoefficient(10,9)
利用Sequence()產生BinomialCoefficient(10,1),.....,BinomialCoefficient(10,10)
Sequence(BinomialCoefficient(10,i),i,1,10)
Sequence(nCr(10,i),i,1,10)
Geogebra 排列指令
nPr(number,number)
nPr(10,1) yields 10
nPr(10,2) yields 10*9
nPr(10,3) yields 10*9 *8
利用Sequence()產生nPr(10,1),.....,nPr(10,10)
Sequence(nPr(10,i),i,1,10)
https://thbu5.thb.gov.tw/page?node=7679d204-1f64-4913-96ae-e80395aeb976
https://www.youtube.com/watch?v=leL4H8kHhVc
Geogebra 因式分解指令
Factors( <Polynomial> ) yields {factor, exponent}
Factors(x^3-1) yields {{x-1,1},{x^2+x+1,1}}
Factors( <Number> )
Gives matrix of the type
(prime_1,exponent_1)
(prime_2,exponent_2)
......
Factors(1024) yields (2 10)
Factor( <Polynomial> ) Factors the polynomial.
Factors(x^3-1) yields (x-1)(x^2+x+1)
Factors over irrationals
Factors over complex irrationals.
國八理化【觀念】光的反射
用Geogebra 動態繪出等比數列(G.P.)
1. 繪出數列 2,4,8,16,...
Geogebra code
a1=2
r=2
n=Slider(1,10,1) #Slider(min,max,step)
Sequence(a1*r^(i-1), i,1,n)
Sequence((i,a1*r^(i-1)),i,1,n) #將數列畫在座標上
Text(a1*r^(n-1),(n,0)) #在座標(n,0)顯示數列的值
StartAnimation(n) #將n變為動畫
Line((1,a1),(2,a1*r))
Lab1. 繪出數列 3,9,27,....
用Geogebra 動態繪出等差數列(A.P.)
1. 繪出數列 2,4,6,8,...
Geogebra code
a1=2
d=2
n=Slider(1,10,1) #Slider(min,max,step)
Sequence(a1+(i-1)*d, i,1,n)
Sequence((i,a1+(i-1)*d),i,1,n) #將數列畫在座標上
Text(a1+(n-1)*d,(n,0)) #在座標(n,0)顯示數列的值
StartAnimation(n) #將n變為動畫
Line((1,a1),(2,a1+d))
Lab1. 繪出數列 3,6,9,12,....
https://www.youtube.com/watch?v=1t7_xNlG0DQ