http://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Pythagorean.svg

a bc

a, b c

ca b

http://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B5%E0%B8%97%E0%B8%B2%E0%B9%82%E0%B8%81%E0%B8%A3%E0%B8%B1%E0%B8%AA

n

ca b

A B C

C

A B

The Pythagorean Proposition

http://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Pythagoras-2a.gif

http://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Pythag_anim.gif

http://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Pythagorean_graphic_(2).PNG

a, b c a bc

a b

a, b c ab c a b °

Euclid's Elements

ABC a,b c a b c

a b

a b

c

- -a b

,c

• a b c

• a b < c

• a b > c

0, 1, 5, -7, , , A

B

A

B

1.

2.

-

1 5

1.

- -

2. , -, -

- - - - - - - - (1)

1) 10

- - - - - - - - (2)

10

2) 1) - - - - - - - - --

- - - - - - - -(1)

1) 1000

- - - - - - - - (2)

1000

1) 10

- - - - - - - - (3)

10

2) 3) - - - - - - - -- -

2

2

1 2

1 2

1 4

1 2

1 2

1.4 1.5

1.4 1.5

1.4 1.5

1.41 1.42

1.1 1.2 1.3 1.4 1.5

1.21 1.44 1.69 1.96 2.25

1.41 1.42 1.43

1.9881 2.0164 2.0449

1.414 1.415

1.4142

1.4143

1.41421 1.41422

1.411 1.412 1.413 1.414 1.415

1.990921 1.993744 1.996569 1.999396 2.002225

1.4141 1.4142 1.4143

1.99967881 1.99996164 2.00024449

1.41421 1.41422

1.9999899241 2.0000182048

1.414213562373095048801688724209...

2

1) 1.234567891011121314

2) 3.4323223222...

3) 16.79779777977779...

4) -4.399339933399...

3.141592653589793238462...

3.1416 3.142

2

- 2

-

1

- 1

2

2 -

1.

1

900

900 --

2

784

784 - -

3

2.

15 16

10 9

165 169

1.3 4

2. 13 9 16 16

3.5

3. 13 12.96 13.69

3.60

3 4

9 13 16

3.5 3.6 3.7

12.25 12.96 13.00 13.69

3.60 3.61

12.9600 13.0000 13.0321

4. 13 12.9600 13.0321 13.0321

3.605

5. 13 13.003236 12.996025

3.606

3.61

3.605 3.606

12.996025 13.000000 13.003236

3.

1 100

10

11

12

13

14

15

16

3.162

3.317

3.464

3.606

3.742

3.873

4.000

100

121

144

169

196

225

256

10.000

1.331

1.728

2.197

2.744

3.375

4.096

0.1000

0.0909

0.0833

0.0769

0.0714

0.0667

0.0625

3

3.1

=

x + 2 = 59 x 8 – 11 = -3

xax + b = 0 a, ba # 0

a = b b = a a b

1. a + b = c c = a = b2. x – 3 = 2x + 7 2x + 7 = x – 3

a = b b = c a = ca, b c

x = 5 + 7 5 + 7 = 12 x = 12

x = -3y -3y = 0.5 x = 0.5

3

-7

7

a = b a + c = b + ca, b c

1. a = 5 a + 3 = 5 + 3

2. x + 7 = 2 (x + 7) -7 = 2 -

3

a =b ca = cb a, b c

1. m + 1 = 2n 3(m + 1) = 3(2n)

2. -3x = 15-3x = 15

-1

-3

-3 -33

2x = 0 1x+ 3 = 0 8y – 11 = 9y + 7

2x – 5 = 0 -4y – 5 = 0 0

2

15x + 9 = 6915x + 9 = 69

9

15x + 9 – 9 = 69 – 915x = 60

15

15x – 15 = 60 – 15

X = 4

.

...

0 1" "

x y

http://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:FuncionLineal02.svg

m

by x2, y1/3, xy

( ) x y

2n

a1,a2,...,an x1,x2,...,xn

b3

x1,x2,x3

x,y,z

n–1 (hyperplane) n

A BA, B, C

1A ≥ 0

(simultaneous equations)

t m = V/Tx (VU−WT) / V y

(WT−VU) / T

T = p−h, U = h, V = q−k, W = k

t 0 (h, k) 1 (p, q) t 0

1(interpolation) t

(extrapolation)

2

AB AB

X Y

AB