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Title: Geometry in a nutshell


Khriss - September 23, 2009 03:25 AM (GMT)
I randomly decided to write about Geometry, lol.

CODE
Table of Contents:
1. Basic Geometry ....... [BEO]
2. Polygons ............. [PEO]
3. Relations and Sizes .. [REO]
4. 3D Geometry .......... [3EO]
5. Greek Vocabulary ..... [GVO]

1. Basic Geometry [BEO]

{Building Blocks} = {Point, Line, Plane, Space}
Point; 0D, a location
Line; 1D, consists of 2+ collinear points
Plane; 2D, consists of 3+ noncollinear points at the same depth
Space; 3d, consists of 3+ noncollinear points of different depth

{Line}            = {Line Segment, Ray, Line}
Line Segment; 2 endpoints
Ray        ; 1 endpoint
Line      ; 0 endpoints

{Line Pairs}      = {Intersecting, Parallel, Perpendicular, Skew}
Intersect  ; Lines intersect
Perpendicular; Lines intersect at a right angle
Parallel    ; Lines do not intersect and are on the same plane
Skew        ; Lines do not intersect and are on different planes

{Angle}           = {right, obtuse, acute, straight, interior}; two rays with the same vertex
Right  ;  90 Degrees
Obtuse  ; >90 Degrees
Acute  ; <90 Degrees
Straight; 180 degrees
Inscribed; Angle with vertex on edge of circle
Interior; Angle with vertex inside circle

Circle:
Origin      ; Center of the circle
Chord      ; A line segment across
Diameter    ; Chord across the origin
Radius      ; Distance from the origin
Circumference; Distance around
Arc        ; A partition of the circumference
Sector      ; A wedge
Tangent    ; Line perpendicular to radius


2. Polygons [PEO]

{Polygons}       = {regular, equiangular, equilateral
                   convex, concave}
Equiangular; All angles congruent
Equilateral; All sides congruent
Regular  ; Equiangular and equilateral
Convex    ; A stright line can only cross two sides
Concave  ; A straight line *can* cross more than two sides

{Polygon Anatomy}= {Side, Vertex, Diagonal, Interior Angle
                   Exterior Angle}
Side        ; A line segment composing the polygon
Vertex      ; Point where sides meet
Diagonal    ; A line connecting two vertices that isn't a side
Interior Angle; Angle inside the polygon
Exterior Angle; Angle external to the polygon

Name         |Sides|Angles|Verticles|Diagonals|
Triangle     |  3  |   3  |    3    |    3    |
Quadrilateral|  4  |   4  |    4    |    2    |
Pentagon     |  5  |   5  |    5    |    5    |
Hexagon      |  6  |   6  |    6    |    9    |
Heptagon     |  7  |   7  |    7    |   14    |
Octagon      |  8  |   8  |    8    |   20    |
Nanagon      |  9  |   9  |    9    |   27    |
Decagon      | 10  |  10  |   10    |   35    |
*Degrees(Angles) = (N-2)180d
*Diagnols        = N(N-3)/2
*Triangles       = N-2

{Triangle}       = {scalene, isosceles, equilateral
                 ;acute, obtuse, right}
Scalene  ; No  sides are equal
Isosceles; Two sides are equal (equal sides, legs; odd side, base)
Equilateral; All sides are equal (angles = 60d) (always acute)
Acute    ; All angles are acute
Obtuse    ; One angle is obtuse
Right    ; One angle is right

{Quadrilateral}  = {square, rectangle, parallelogram, trapezoid
                   rhombus, kite}
Parallelogram; Opposite sides parallel and congruent
-Rectangle  ; 4 right angles
-Rhombus    ; A parallelogram with four equal sides
--Square    ; Rectangle and Rhombus
Trapezoid  ; Only one pair of parallel lines
Kite        ; Two pairs of equal adjacent sides

Area:
Parallelogram; Base*Height
Triangle    ; Base*Height/2
Circle      ; πr^2
Trapezoid  ; (base1+base2)h/2
Ellipse    ; π*r1*r2


3. Relations and Sizes [REO]

Congruent; Exactly the same
Similar; Same angles and sides in proportion

Expondents; x^x
-Squares; x^2
-Cubes  ; x^3

Pythagreon Theorem; a^2 + b^2 = c^2 (for right triangles)
A&B; Leg
C; Hypotenuse


4. 3D Geometry [3EO]

{3D}              = {length, width, height}

{Space Figure}    = {polyhedron, cylinder, cone, sphere}
Polyhedron; Bounded by plane polygons
Cylinder; Tcongruent circular bases
Cone    ; One vertex and a circular base
Sphere  ; All points in space equidistant from the center

{Polyhedron}      = {prism, pyramid}
Prism; Two parallel congruent bases & parallelogramical lateral
        faces
Pyramid; Polygon base and triangle faces sharing vertex

Volume:
Prism  ; Base*Height
Pyramid; Base*Height/3
Cylinder; πr^2*Height
Cone    ; πr^2*Height/3
Sphere  ; (πr^2)4/3
Ellipsoid; π(r1*r2*r3)4/3

Area:
Prism  ; (Circumbase)*height + 2(base area)
Sphere  ; 4πr^2
Cylinder; 2πr^2 + 2πr*height

5. Greek Vocabulary [GVO]

1  ; Un
2  ; Do
3  ; Tri
4  ; Tetra
5  ; Penta
6  ; Hexa
7  ; Hepta
8  ; Octa
9  ; Ennea
10  ; Deca
13  ; Tridecagon
19  ; Enneadecagon
20  ; Icosa
25  ; Icosikaipentagon
30  ; Trianconta
40  ; Tetraconta
50  ; Pentaconta
60  ; Hexaconta
70  ; Heptaconta
80  ; Octaconta
90  ; Enneaconta
100; Hecto
1000; Chilia
10000; Myria

Lucius - September 24, 2009 01:00 AM (GMT)
I don't have the patience for all of that.

Dark Overlord Zack - September 24, 2009 01:14 AM (GMT)
you know, this is actually pretty good if you're in need of a formula chart or whatever.

Thanks Khriss.

Isaac55 - September 24, 2009 01:18 AM (GMT)
Heh, I wish I had made geometry this year.

Denning Rosewater - September 24, 2009 10:16 PM (GMT)
Last few posts were deleted due to redundancy and not really contributing to the discussion in the slightest.

As for the article, I like it. It covers the basics well, and even explains the shapes, # of sides, etc. Excellent for a basic rubric; sure it'd help a younger member here who was going to be taking geometry soon. Something like this would've sure helped me out, I tell you...

carlantis25 - September 24, 2009 11:44 PM (GMT)
thanks this will really help out on a test. but one question remains why did you do this do you not have a better waste of time?????? such as reading the BS posts in the spam folder alot of the old stuff is funnier than when Will Smith forgot his lines on a LIVE telethon *skips to flash back* (family guy humor)




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