2020年6月26日星期五

求過直徑上兩點(1,2),(3,4)的圓方程式

1.圓心O=(2,3)
r=sqrt( (3-2)^2+(4-2)^2)=sqrt(2)

(x-2)^2+(y-3)^2=2

2. 向量法
半徑的圓周角＝90度
(x-1,y-2).(x-3,y-4)=0
(x-1)(x-3)+(y-2)(y-4)=0 - 直徑式
x^2-4x+3+y^2-6y+8=0 - 一般式
(x-2)^2+(y-3)^2-1-1=0
(x-2)^2+(y-3)^2=2 - 標準式

圓的切線

C:(x-1)^2＋(y-2)^2=4
A=(1,4)
B=(2,4)

1.過A求圓的切線(check A on C)
方法一.點到直線距離=r     ( d(O,L)=r )
check A on C ?
(1-1)^2＋(4-2)^2=4, so A on C
L: y-4=m(x-1)
    mx-y-m+4=0
O=(1,2), r=2
d(O,L)=|m-2-m+4|/sqrt(m^2+1)=2
2/sqrt(m^2+1)=2
2=2 * sqrt(m^2+1)
m=0
L: y-4=0

方法二. 直線的向量與半徑的向量內積為零     ( L.r=0 )
vector L=(x-1,y-4)
vector r=A-O=(0,2)
L.r=0

2(y-4)=0

y-4=0

2.過B(2,4)求圓的切線(check B doesn't on C)

方法一.點到直線距離=r     ( d(O,L)=r )

L: y-4=m(x-2)
    mx-y-2m+4=0
O=(1,2), r=2
d(O,L)=|m-2-2m+4|/sqrt(m^2+1)=2
|-m+2|=2*sqrt(m^2+1)
m^2-4m+4=4(m^2+1)
3m^2+4m=0
m=0,-4/3
y-4=0
or
y-4=-4/3(x-2)
4x+3y-8-12=0
4x+3y-20=0

方法二. 直線的單位法向量與半徑的向量內積=半徑     ( n.r=半徑 )
L: y-4=m(x-2)
    mx-y-2m+4=0
vector n=(m,-1)/sqrt(m^2+1)
vector r=(x-1,y-2)
n.r=2
|m(x-1)-(y-2)|/sqrt(m^2+1)=2
|mx-y-m+2|=2*sqrt(m^2+1)
|2m-4-m-2|=2*sqrt(m^2+1)
|m-2|^2=4(m^2+1)
m^2-4m+4=4m^2+4
3m^2+4m=0
m=0,-4/3

y-4=0
or
y-4=-4/3(x-2)
4x+3y-8-12=0
4x+3y-20=0

python regression

https://towardsdatascience.com/machine-learning-polynomial-regression-with-python-5328e4e8a386

2020年6月17日星期三

Geogebra 點/線與圓的關係

1.觀察點與圓的位置關係

h=1

k=2

r=2

(x-h)^2+(y-k)^2=r^2

A=(1,2)

B=(1,4)

C=(1,6)

2. 將圓心,半徑改為滑桿

h=slider(-5,5,.01)

k=slider(-5,5,.01)

r=slider(-5,5,.01)

(x-h)^2+(y-k)^2=r^2

A=(1,2)

B=(1,4)

C=(1,6)

個別點h, k, r 開始動畫,觀察圓的變化

3.圓上一點切線只有一條

m=slider(-5,5,.01)

y-4=m(x-1)

h=1

k=2

r=2

(x-h)^2+(y-k)^2=r^2

4.圓外一點切線只有一條

B=(2,4)

y-y(B)=m(x-x(B))
m=slider(-5,5,.01)

h=1

k=2

r=2

(x-h)^2+(y-k)^2=r^2

5.用Excel

python scraping

https://github.com/REMitchell/python-scraping/blob/master/Chapter01_BeginningToScrape.ipynb

2020年6月16日星期二

python plot

[資料分析&機器學習] 第2.5講：資料視覺化(Matplotlib, Seaborn, Plotly)

https://medium.com/jameslearningnote/%E8%B3%87%E6%96%99%E5%88%86%E6%9E%90-%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92-%E7%AC%AC2-5%E8%AC%9B-%E8%B3%87%E6%96%99%E8%A6%96%E8%A6%BA%E5%8C%96-matplotlib-seaborn-plotly-75cd353d6d3f

matplotlib
https://blog.techbridge.cc/2018/05/11/python-data-science-and-machine-learning-matplotlib-tutorial/

[第 18 天] 資料視覺化 matplotlib
https://ithelp.ithome.com.tw/articles/10186484

歷屆試題

109 c
7.
(x-4)^2/25+(y+2)^2/144=1 求頂點，正焦弦長

中心點O=(4,-2)
長軸a=12 on y axis
短軸b=5
頂點
O+(0,12)
O-(0,12)
O+(5,0)
O-(5,0)
焦距c=sqrt(a^2-b^2)
焦點O+(0,c)
焦點O+(0,-c)
正焦弦長 d=2b^2/a

10.
x+2y-6>=0
x+y-10<=0

2<=x<=9
求解的面積

x+2y-6=0
x|2 |9
-------------
y|2 |-3/2

x+y-10=0
x|2 |9
-------------
y|8 |1

11.
f(x)=2cos(3x)-1
a=f(x)與x軸的交點數
b=f(x) max
solve ab=?

-1<=cos3x<=1

-2-1<=cos3x-1<=2-1
-3<=cos3x-1<=1
b=f(x) max=1

cosx period= 2pi
cos3x period=2pi/3

13.
f(x)=x^3-3x^2-24x+32 on [-3,3]
m=f(x) max, n=f(x) min, solve m-n=?

2020年6月15日星期一

New connections between Dynamic Systems

Vasili Bernik - New connections between Dynamic Systems

https://www.youtube.com/watch?v=_yODaV3pmdk&t=722s

Quantum Mechanics

Lecture 3 | Modern Physics: Quantum Mechanics (Stanford)

https://www.youtube.com/watch?v=epzh76hNl8I

complete lesson (Classical Mechanics)
https://www.youtube.com/view_play_list?p=189C0DCE90CB6D81

Ising model

Arindam Kumar Chatterjee

https://www.youtube.com/watch?v=kvf7aUPZCWk

Arindam Kumar Chatterjee
https://drive.google.com/drive/folders/0B22xwwpFP6LNNW5LNDAzalZMclU

Jos Thijssen

https://www.youtube.com/watch?v=hX_FrS5XO3I

2020年6月12日星期五

machine learning polynomial regression

https://towardsdatascience.com/machine-learning-polynomial-regression-with-python-5328e4e8a386

2020年6月9日星期二

vim unicode 亂碼

:set encoding-utf8

https://blog.gtwang.org/tips/vim-working-with-unicode/

2020年6月8日星期一

install software in ubuntu

Latex
sudo apt-get install texlive-full

JabRef

octave

sudo apt-get install flatpak

flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo

flatpak install flathub org.octave.Octave

flatpak run org.octave.Octave

https://ubuntuqa.com/zh-tw/article/9289.html

https://blog.gtwang.org/linux/ubuntu-compile-and-install-octave/

maxima
sudo apt-get install maxima

gvim
sudo apt-get install gvim

notepadqq

anocanda
https://docs.anaconda.com/anaconda/install/linux/

R

geogebra

wine

Line