History,applications,algebra and mathematical form of plane in mathematics (presentation.ppt)

SLIDE33 SLIDE25 SLIDE26 SLIDE27 SLIDE28 SLIDE29 SLIDE10 SLIDE2 SLIDE31 SLIDE32 SLIDE24 SLIDE23 SLIDE22 SLIDE17 SLIDE19 SLIDE18 SLIDE8 SLIDE41 SLIDE40 SLIDE39 SLIDE35 SLIDE9 SLIDE21 SLIDE20 SLIDE30 SLIDE38 SLIDE37 SLIDE36 SLIDE11 SLIDE3 SLIDE12 SLIDE13 SLIDE14 SLIDE16 SLIDE4 SLIDE5 SLIDE6 SLIDE7 SLIDE15

Presentation on PLANE Name: Nabeela Hayat Department: Bioinformatics Frontier Women University (Town Campus)

Table of contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Definition of Plane ,[object Object],[object Object]

A plane is a flat surface with no thickness. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Plane Shape ,[object Object]

Examples ,[object Object],[object Object]

History ,[object Object],[object Object]

Planes in fiction ,[object Object]

Two-dimensional coordinate system ,[object Object]

Three-dimensional coordinate system ,[object Object],[object Object],[object Object],[object Object]

Orientation and handedness ,[object Object],[object Object],[object Object]

Area of Plane Shapes Triangle Area = ½b×h b = base h = vertical height Rectangle Area = b×h b = breadth h = height Trapezoid (US) Trapezium (UK) Area = ½(a+b)h h = vertical height Ellipse Area = πab Square Area = a2 a = length of side Parallelogram Area = b×h b = breadth h = height Circle Area = πr2 Circumference=2πr r = radius Sector Area = ½r2θ r = radius θ = angle in radians

Equations of plane ,[object Object],[object Object]

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

I) Equations of straight lines ,[object Object],[object Object],Rise Run P1(x1, y1) P1(x2, y2) y1-y2 x1-x2 x y l o

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Ф l x y Ф x y l o o Figure I a b Ф l x y o P2(x2, y2) Ф P1(x1, y1) P3(x2, y1) (x2-x1) (y2-y1) M N Case II Ф l x y o P2(x2, y2) Ф P1(x1, y1) P3(x2, y1) (x2-x1) (y2-y1) M N Case III Ф=0 l x y o Case I

I) Equations of straight lines ,[object Object],[object Object],[object Object],d>0 l x y o l x y o x y o d d d<0 d=0 (A) l ║ x-axis or l ┴ y-axis (B) l ║ x-axis or l ┴ y-axis (C) l ║ x-axis or l ┴ y-axis Figure1 (a) Figure1 (b) Figure1 (c)

I) Equations of straight lines ,[object Object],[object Object],[object Object],d>0 l x y o d (A) l ║ y-axis or l ┴ x-axis Figure2 (a) d<0 l x y o d (B) l ║ y-axis or l ┴ x-axis Figure2 (b) d=0 x y o (B) l ║ y-axis or l ┴ x-axis Figure2 (c)

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

iv) Derivation of Standard Forms of Equations of Straight Lines: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Ф l x y o P(x1,y1) P'(x,y) Point-Slope Form Ф l x y o B(0,b) Slope Intercept Form A(a,0)

iv) Derivation of Standard Forms of Equations of Straight Lines: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Ф l x y o P(x,y) Two-Points Form P1(x1,y1) P2(x2,y2) l x y o (0,b) (a, 0) P(x,y) Two Intercepts Form

iv) Derivation of Standard Forms of Equations of Straight Lines: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Ф l x y o P(x,y) Normal Form B p A 90-Ф Q Ф P'(x,y) l x y o P(x1,y1) Symmetric Form

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

vi) To Transform the General Linear Equation in Standard Forms ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

vi) To Transform the General Linear Equation in Standard Forms ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],l O x y Figure 1(a) l O x y Figure 1(b) P(x1, y1) P1(x1, y') P(x1, y1)

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],l O x y Figure 1(a) P(x1, y1) l O x y Figure 1(b) P(x1, y1) P1(x1, y') Ф N M d Ф Ф

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],l O x y Figure 1 P(x1, y1) Q(x2, y2) d 1 l 2

I) Equations of straight lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],*Trapezoid: A four sided shape in which no sides are parallel l O x y Figure 1 P1(x1, y1) A(x1, 0) P2(x2, y2) P3(x3, y3) C(x1, 0) B(x1, 0)

II) Two and Three Straight Lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

II) Two and Three Straight Lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],l x y Figure 1 1 l 2 Φ Φ 2 1 θ O

II) Two and Three Straight Lines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

II) Two and Three Straight Lines ,[object Object],[object Object],[object Object],[object Object],[object Object],F G E D A(x1, y1) C(x3, y3) B(x2, y2) Figure 1(a) F o E D A(x1, y1) C(x3, y3) B(x2, y2) Figure 1(b)

II) Two and Three Straight Lines ,[object Object],[object Object]

VI) Equation of straight lines in Matrix Form ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],x y x y

End of the presentation THANK YOU Give A BIG Hand

History,applications,algebra and mathematical form of plane in mathematics (presentation.ppt)

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to History,applications,algebra and mathematical form of plane in mathematics (presentation.ppt)

Similar to History,applications,algebra and mathematical form of plane in mathematics (presentation.ppt) (20)

Recently uploaded

Recently uploaded (20)

History,applications,algebra and mathematical form of plane in mathematics (presentation.ppt)