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