-Coincidence of face and line
-dihedral angle and solid angle
-Square, cuboid, parallelepiped
-Tetrahedrons and other pyramids
prism
-octahedron, dodecahedron, icosahedron
-Cones, cylinders
Used as an emphasis in various derogatory words.
-Other quadric surfaces: ellipsoid of revolution, ellipsoid, paraboloid, hyperboloid.
Self-evident truth
There are four axioms in solid geometry.
Axiom 1 If two points on a straight line are on a plane, then the straight line is on this plane.
Axiom 2 passes through three points that are not on a straight line, and there is only one plane.
Axiom 3 If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.
Axiom 4 Two lines parallel to the same line are parallel.
Cubic figure
Solid geometry formula
Name symbol area s volume v
The side length of cube a is s = 6a 2 v = a 3.
Cuboid a- length s = 2 (ab+AC+BC) v = ABC.
B width
C height adjustment
Prism s- bottom area v = sh
up level
The bottom area of pyramid s v = sh/3.
up level
Prism S 1 and S2- upper and lower bottom areas v = h [s1+S2+√ (s12)/2]/3.
up level
Prismatoid S 1—— Upper and lower area v = h (s 1+S2+4s0)/6.
S2-bottom area
S0-middle cross-sectional area
up level
R- base radius of cylinder c = 2 π r v = s base h=∏rh.
up level
C—— perimeter of bottom surface
S bottom-bottom area s bottom = π r 2
S side-lateral area s side = ch.
S table-surface area s table = CH+2S bottom
S base = π r 2
Hollow cylinder R—— radius of external circle
R—— radius of inner circle
H- height v = π h (r 2-r 2)
R base radius of straight cone
H- height v = π r 2h/3
Cone r- upper bottom radius
R- bottom radius
H-height v = π h (r 2+RR+r 2)/3.
Sphere r radius
D- diameter v = 4/3 π r 3 = π d 2/6.
Ball missing h- ball missing height
Sphere radius
A—— The radius of the ball's base is a2 = h (2r-h) v = π h (3a2+H2)/6 = π h2 (3r-h)/3.
Tables r 1 and R2-the radius of the table top and table top.
H- height v = π h [3 (r 12+R22)+H2]/6.
Circle radius
D—— ring diameter
R—— the section radius of the ring.
D—— the cross-sectional diameter of the ring v = 2π 2rr 2 = π 2dd 2/4.
Bucket D—— diameter of barrel belly
D—— diameter of barrel bottom
H—— bucket height v = π h (2d 2+D2)/ 12 (the bus is circular, and the center of the circle is the center of the bucket).
V = π h (2D 2+DD+3D 2/4)/ 15 (bus is parabolic)
Plane analytic geometry includes the following parts.
cartesian coordinates
1. 1 directed line segment
1.2 Cartesian coordinates of points on a straight line
Several Basic Formulas of 1.3
Rectangular coordinates of points on 1.4 plane
Basic principle of 1.5 projection
Several Basic Formulas of 1.6
Two curves and agenda
2. The definition of1curve directly solves the coordinate equation.
2.2 Find each curve and find its equation.
2.3 Known curve equation, describe the curve.
2.4 Intersection of curves
Three straight lines
3. 1 Angle and slope of straight line
3.2 linear equation
Y=kx+b
3.3 Directed distance from straight line to point
3.4 Plane Region Represented by Binary Linear Inequality
3.5 the relative position of two straight lines
3.6 Conditions for Binary Equation to Express Two Straight Lines
3.7 Relative position of three straight lines
3.8 Linear system
Siyuan
4. Definition of1circle
4.2 Equation of Circle
4.3 Relative position of point and circle
4.4 Tangent of a circle
4.5 Chords and Polar Lines of a Point on a Circle
4.6 *** axis circulation system
4.7 Inverse evolution on the plane
Five ellipses
5. Definition of1ellipse
5.2 An ellipse can be obtained by cutting a conical surface with a plane.
5.3 Standard Equation of Ellipse
5.4 Basic properties and related concepts of ellipse
5.5 Relative position of point and ellipse
5.6 Tangents and normals of ellipses
5.7 Points on the tangent and polar lines of an ellipse
5.8 area of ellipse
Six hyperbola
6. Definition of1hyperbola
6.2 A hyperbola can be obtained by cutting a conical surface with a plane.
6.3 standard equation of hyperbola
6.4 Basic properties and related concepts of hyperbola
6.5 equilateral hyperbola
6.6 *** Yoke Hyperbola
6.7 Relative position of point and hyperbola
6.8 Tangents and normals of hyperbola
6.9 the tangent of hyperbola and the point on the polar line
Seven parabolas
7. Definition of1parabola
7.2 A parabola can be obtained by cutting a conical surface with a plane.
7.3 standard equation of parabola
7.4 Basic properties and related concepts of parabola
7.5 Relative position of point and parabola
7.6 Tangents and normals of parabolas
7.7 Points on the tangent line and polar line of parabola
7.8 Area of Parabolic Arch
Eight-coordinate transformation and the general theory of quadratic curve
8. The concept of1coordinate transformation
8.2 Translation of Axis
8.3 Simplify the curve equation by translation
8.4 Standard Equation of More General Conic Curve
8.5 Rotation of coordinate axis
8.6 General formula of coordinate transformation
8.7 Classification of curves
8.8 Invariants of Quadratic Curve under Cartesian Coordinate Transformation
8.9 curve of binary quadratic equation
8. Simplification of10 quadratic equation
8. 1 1 Conditions for Determining Quadratic Curve
8. 12 conic system
Nine-parameter equation
Ten polar coordinates
Eleven oblique coordinates