All mathematical formulas from elementary school to high school
1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours
Total workload ÷ working time = working efficiency
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Calculation formula of mathematical graphics in primary schools
1, squared: c perimeter s area a side length perimeter = side length× 4c = 4a area = side length× side length s = a× a.
2. Cube: v: volume A: side length surface area = side length × side length× 6s table =a×a×6.
Volume = side length × side length × side length v = a× a× a.
3. Rectangular:
C perimeter s area a side length perimeter = (length+width) ×2 C=2(a+b) area = length × width S=ab.
4. Cuboid
V: volume s: area a: length b: width h: height.
(1) surface area (length× width+length× height+width× height )× 2s = 2 (AB+ah+BH)
(2) volume = length× width× height V=abh
5. Triangle
S area a bottom h height area = bottom x height ÷2 s=ah÷2.
Height of triangle = area ×2÷ base.
Triangle base = area ×2÷ height
6. parallelogram: s area a bottom h height area = bottom x height s=ah.
7. Trapezoid: s area a, upper bottom b, lower bottom h, height area = (upper bottom+lower bottom) × height ÷2 s=(a+b)×h÷2.
8 circle: s plane, c circumference ∏ d= diameter, r= radius.
(1) perimeter = diameter ×∏=2×∏× radius C=∏d=2∏r
(2) area = radius × radius×∈
9. cylinder: v volume h: height s: bottom area r: bottom radius c: bottom circumference.
(1) lateral area = bottom circumference × height.
(2) Surface area = lateral area+bottom area ×2
(3) Volume = bottom area × height
(4) Volume = lateral area ÷2× radius.
10, cone: v volume h height s bottom area r bottom radius volume = bottom area x height÷ 3.
Total number ÷ Total number of copies = average value
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
And folding problems.
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
Tree planting problem
1. The problem of planting trees on unclosed lines can be mainly divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1 = total length-1.
Total length = plant spacing × (number of plants+1)
Plant spacing = total length ÷ (number of plants+1)
2. The quantitative relationship of planting trees on the closed line is as follows
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
The question of profit and loss
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount problem
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
Length unit conversion
1 km = 1 000m1m = 10 decimeter.
1 decimeter =10cm1m =10cm.
1 cm = 10/0mm
Area unit conversion
1 km2 = 100 hectare
1 ha = 1 10,000 m2
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
Volume (volume) unit conversion
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cm3 = 1 ml
1 m3 = 1000 liter
Weight unit conversion
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
Rmb unit conversion
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
Time unit conversion
1 century = 100 1 year =65438+ February.
The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.
Abortion (30 days) includes: April \ June \ September \165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours 1 hour =60 minutes
1 min = 60s 1 hr = 3600s.
Calculation formula of perimeter, area and volume of mathematical geometry in primary schools
1, the perimeter of the rectangle = (length+width) ×2 C=(a+b)×2.
2. The circumference of a square = side length ×4 C=4a.
3. Area of rectangle = length× width S=ab
4. Square area = side length x side length s = a.a = a.
5. Area of triangle = base × height ÷2 S=ah÷2.
6. parallelogram area = bottom x height S=ah
7. trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) h ÷ 2.
8. Diameter = Radius× 2D = 2r Radius = Diameter ÷2 r= d÷2
9. The circumference of a circle = π× diameter = π× radius× 2c = π d = 2π r.
10, area of circle = π× radius× radius.
Common junior high school mathematics formulas
1 There is only one straight line at two points.
The line segment between two points is the shortest.
The complementary angles of the same angle or equal angle are equal.
The complementary angles of the same angle or the same angle are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7 Parallel axiom passes through a point outside a straight line, and there is only one straight line parallel to this straight line.
If both lines are parallel to the third line, the two lines are also parallel to each other.
The same angle is equal and two straight lines are parallel.
The internal dislocation angles of 10 are equal, and the two straight lines are parallel.
1 1 are complementary and two straight lines are parallel.
12 Two straight lines are parallel and have the same angle.
13 two straight lines are parallel, and the internal dislocation angles are equal.
14 Two straight lines are parallel and complementary.
Theorem 15 The sum of two sides of a triangle is greater than the third side.
16 infers that the difference between two sides of a triangle is smaller than the third side.
The sum of the internal angles of 17 triangle is equal to 180.
18 infers that the two acute angles of 1 right triangle are complementary.
19 Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
Inference 3 The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
2 1 congruent triangles has equal sides and angles.
Axiom of Angular (SAS) has two triangles with equal angles.
The Axiom of 23 Angles (ASA) has the congruence of two triangles, which have two angles and their sides correspond to each other.
The inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
The axiom of 25 sides (SSS) has two triangles with equal sides.
The hypotenuse and right-angle axiom (HL) have two right-angle triangles, and the hypotenuse and right-angle correspond to each other.
suit
Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
Theorem 2 is a point with equal distance on both sides of an angle, which is on the bisector of this angle.
The bisector of an angle 29 is the set of all points with equal distance to both sides of the angle.
The nature theorem of isosceles triangle 30 The two base angles of isosceles triangle are equal (that is, equilateral and equiangular).
3 1 Inference 1 The bisector of the vertices of an isosceles triangle bisects the base and is perpendicular to the base.
The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide with each other.
Inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60.
34 Decision Theorem of Isosceles Triangle If a triangle has two equal angles, then these two angles
The opposite sides are also equal (equal angle and equal side)
Inference 1 A triangle with three equal angles is an equilateral triangle.
Inference 2 An isosceles triangle with an angle equal to 60 is an equilateral triangle.
In a right triangle, if an acute angle is equal to 30, then the right side it faces is equal to the hypotenuse.
one half
The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.
Theorem 39 The distance between the point on the vertical line of a line segment and the two endpoints of the line segment is equal.
The inverse theorem and the point where the two endpoints of a line segment are equidistant are on the middle vertical line of this line segment.
The perpendicular bisector of the 4 1 line segment can be regarded as the set of all points with equal distance from both ends of the line segment.
Theorem 42 1 Two graphs symmetric about a line are conformal.
Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is perpendicular to the connecting line of the corresponding points.
bisector
Theorem 3 Two graphs are symmetrical about a straight line. If their corresponding line segments or extension lines intersect,
Then the intersection point is on the axis of symmetry.
45 Inverse Theorem If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then these two graphs
A figure is symmetrical about this line.
46 Pythagorean Theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C,
That is a 2+b 2 = c 2.
47 Pythagorean Theorem Inverse Theorem If the lengths of three sides of a triangle A, B and C are related, then A 2+B 2 = C 2,
So this triangle is a right triangle.
The sum of the quadrilateral internal angles of Theorem 48 is equal to 360.
The sum of the external angles of the quadrilateral is equal to 360.
The theorem of the sum of internal angles of 50 polygons is that the sum of internal angles of n polygons is equal to (n-2) × 180.
5 1 It is inferred that the sum of the external angles of any polygon is equal to 360.
52 parallelogram property theorem 1 parallelogram diagonal equality
53 parallelogram property theorem 2 The opposite sides of parallelogram are equal
It is inferred that the parallel segments sandwiched between two parallel lines are equal.
55 parallelogram property theorem 3 diagonal bisection of parallelogram.
56 parallelogram decision theorem 1 Two groups of parallelograms with equal diagonals are parallelograms.
57 parallelogram decision theorem 2 Two groups of parallelograms with equal opposite sides are parallelograms.
58 parallelogram decision theorem 3 A quadrilateral whose diagonal is bisected is a parallelogram.
59 parallelogram decision theorem 4 A group of parallelograms with equal opposite sides are parallelograms.
60 Rectangle Property Theorem 1 All four corners of a rectangle are right angles.
6 1 rectangle property theorem 2 The diagonals of rectangles are equal
62 Rectangular Decision Theorem 1 A quadrilateral with three right angles is a rectangle.
63 Rectangular Decision Theorem 2 Parallelograms with equal diagonals are rectangles
64 diamond property theorem 1 all four sides of the diamond are equal.
65 Diamond Property Theorem 2 Diagonal lines of diamonds are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.
66 Diamond area = half of diagonal product, that is, S=(a×b)÷2.
67 diamond decision theorem 1 A quadrilateral with four equilateral sides is a diamond.
68 Diamond Decision Theorem 2 Parallelograms whose diagonals are perpendicular to each other are diamonds.
69 Theorem of Square Properties 1 All four corners of a square are right angles and all four sides are equal.
70 Square Property Theorem 2 Two diagonal lines of a square are equal and bisected vertically, and each
Diagonal lines bisect a set of diagonal lines.
Theorem 7 1 1 is congruent with respect to two centrosymmetric graphs.
Theorem 2 About two graphs with central symmetry, the connecting lines of symmetric points both pass through the symmetric center and are
Symmetric central bisection
Inverse Theorem If a straight line connecting the corresponding points of two graphs passes through a point and is equally divided by it,
Then these two graphs are symmetrical about this point.
The property theorem of isosceles trapezoid is that two angles of isosceles trapezoid on the same base are equal.
The two diagonals of an isosceles trapezoid are equal.
76 isosceles trapezoid decision theorem A trapezoid with two equal angles on the same base is an isosceles trapezoid.
A trapezoid with equal diagonal lines is an isosceles trapezoid.
Theorem of Equal Segment of Parallel Lines If a group of parallel lines have equal segments on a straight line,
Then the line segments cut on other straight lines are equal.
79 Inference 1 A straight line passing through the midpoint of one waist of a trapezoid and parallel to the bottom will bisect the other waist.
Inference 2 A straight line passing through the midpoint of one side of a triangle and parallel to the other side will bisect the third side.
The median line theorem of 8 1 triangle The median line of a triangle is parallel to the third side and equal to half of it.
The trapezoid midline theorem is parallel to the two bases and is equal to half the sum of the two bases.
L=(a+b)÷2 S=L×h
83 (1) Basic Properties If a:b=c:d, then ad=bc If ad=bc, then A: B = C: D.
84 (2) Combinatorial Properties If A/B = C/D, then (A B)/B = (C D)/D.
85 (3) Isometric Property If A/B = C/D = … = M/N (B+D+…+N ≠ 0), then (a+c+…+m)
/(b+d+…+n)=a/b
Proportional theorem of dividing line segments by parallel lines Three parallel lines cut two straight lines to get the corresponding line segments.
proportion
It is inferred that a straight line parallel to one side of a triangle cuts the other two sides (or extension lines on both sides), and the result is
Proportional to the line segment.
Theorem 88 If a straight line cuts two sides of a triangle (or the extension lines of two sides), the corresponding straight line is obtained.
If the line segments are proportional, then this line is parallel to the third side of the triangle.
A straight line parallel to one side of a triangle and intersecting the other two sides of the triangle.
These three sides are proportional to the three sides of the original triangle.
Theorem 90 A straight line parallel to one side of a triangle intersects the other two sides (or extension lines of both sides).
The triangle is similar to the original triangle.
9 1 similar triangles's decision theorem 1 Two angles are equal and two triangles are similar (ASA)
Two right triangles divided by the height on the hypotenuse are similar to the original triangle.
Decision Theorem 2: Two sides are proportional and the included angle is equal, and two triangles are similar (SAS).
Decision Theorem 3 Three sides are proportional and two triangles are similar (SSS)
Theorem 95 If the hypotenuse and a right angle of a right triangle are the same as those of another right triangle.
The hypotenuse is proportional to the right-angled side, so two right-angled triangles are similar.
96 Property Theorem 1 similar triangles corresponds to a high ratio, corresponding to the ratio of the median line to the corresponding angular bisector.
Ratio equals similar ratio.
97 Property Theorem 2 The ratio of similar triangles perimeter is equal to similarity ratio.
98 Property Theorem 3 The ratio of similar triangles area is equal to the square of similarity ratio.
The sine value of any acute angle is equal to the cosine value of other angles, and the cosine value of any acute angle is equal to it.
Sine value of complementary angle
100 The tangent of any acute angle is equal to the cotangent of other angles, and the cotangent of any acute angle is equal to it.
Tangent value of complementary angle
10 1 A circle is a set of points whose distance from a fixed point is equal to a fixed length.
102 The interior of a circle can be regarded as a collection of points whose center distance is less than the radius.
The outer circle of 103 circle can be regarded as a collection of points whose center distance is greater than the radius.
104 The radius of the same circle or equal circle is the same.
The distance from 105 to the fixed point is equal to the trajectory of a fixed-length point, which is a circle with the fixed point as the center and the fixed length as the radius.
106 and the locus of the point with the same distance between the two endpoints of the known line segment is the middle vertical line of the line segment.
The locus from 107 to a point with equal distance on both sides of a known angle is the bisector of this angle.
The trajectory from 108 to the equidistant point of two parallel lines is parallel to and equidistant from these two parallel lines.
A straight line
Theorem 109 Three points that are not on the same straight line determine a circle.
1 10 vertical diameter theorem divides the chord perpendicular to its diameter into two parts, and divides the two arcs opposite to the chord into two parts.
1 1 1 inference 1
(1) bisects the diameter (not the diameter) of the chord perpendicular to the chord and bisects the two arcs opposite to the chord.
(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.
③ bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.
1 12 Inference 2 The arcs sandwiched by two parallel chords of a circle are equal.
1 13 circle is a centrosymmetric figure with the center of the circle as the symmetry center.
Theorem 1 14 In the same circle or in the same circle, equal central angles have equal arcs and equal chords.
The distance between chords of opposite chords is equal.
1 15 Inference: If two central angles, two arcs, two chords or two chords are on the same or equal circle,
If one group of quantities in the heart distance is equal, then the corresponding other groups are also equal.
Theorem 1 16 The angle of an arc is equal to half its central angle.
1 17 Inference 1 The circumferential angles of the same arc or the same arc are equal; Equal circumferential angle in the same circle or in the same circle.
Circular arcs are also equal.
1 18 Inference 2 The circumferential angle (or diameter) of a semicircle is a right angle; A chord with a circumferential angle of 90 degrees.
It's diameter
1 19 inference 3 if the median line of one side of a triangle is equal to half of this side, then this triangle is
right triangle
120 Theorem The inscribed quadrangles of a circle are diagonally complementary, and any external angle is equal to its internal angle pair.
corner
12 1 ① the intersection of the straight line l and ⊙O is d < r.
(2) the tangent of the straight line l, and ⊙ o d = r.
③ lines l and ⊙O are separated by d > r.
122 the judgment theorem of tangent line is that the straight line passing through the outer end of the radius and perpendicular to the radius is the tangent line of the circle.
line
123 The property theorem of tangent line The tangent line of a circle is perpendicular to the radius passing through the tangent point.
124 Inference 1 A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point.
125 Inference 2 A straight line passing through the tangent and perpendicular to the tangent must pass through the center of the circle.
126 tangent length theorem leads to two tangents of a circle from a point outside the circle. Their tangents are equal in length, and the center of the circle is sum.
The straight line connecting this point bisects the angle between the two tangents.
127 The sum of two opposite sides of a circle's circumscribed quadrilateral is equal.
128 Chord Angle Theorem The chord angle is equal to the circumferential angle of the arc pair it clamps.
129 Inference: If the arc enclosed by two chord tangent angles is equal, then the two chord tangent angles are also equal.
130 intersection chord theorem The length of two intersecting chords in a circle divided by the product of the intersection point is equal.
13 1 Inference: If the chord intersects the diameter vertically, then half of the chord is two lines formed by its divided diameter.
Median proportion of sections
132 tangent theorem leads to the tangent and secant of a circle starting from a point outside the circle, and the tangent length is the secant and circle starting from this point.
The proportional average of the lengths of two intersecting lines.
133 infer two secant lines leading to the circle from a point outside the circle, and this point reaches the intersection of each secant line and the circle.
The product of line segment lengths is equal.
134 If two circles are tangent, then the tangent point must be on the line.
135 ① perimeter of two circles D > R+R ② perimeter of two circles d=R+r ③ intersection of two circles R-R < D < R+R (R > R).
④ inscribed circle D = R-R (R > R) ⑤ two circles contain D < R-R (R > R).
Theorem 136 The intersection of two circles bisects the common chord of two circles vertically.
Theorem 137 divides a circle into n (n ≥ 3);
(1) The polygon obtained by connecting the points in turn is the inscribed regular N polygon of this circle.
(2) A polygon whose vertex is the intersection of adjacent tangents is a circle.
The circumscribed regular n polygon of
Theorem 138 Any regular polygon has a circumscribed circle and an inscribed circle, which are concentric circles.
139 every inner angle of a regular n-polygon is equal to (n-2) ×180/n.
140 Theorem Radius and apothem Divides a regular N-polygon into 2n congruent right triangles.
14 1 the area of the regular n polygon Sn = PNRN/2 P represents the perimeter of the regular n polygon.
142 The area of a regular triangle √ 3a/4a indicates the side length.
143 if there are k positive n corners around a vertex, then the sum of these angles should be 360, because
This k × (n-2) 180/n = 360 is changed to (n-2)(k-2)=4.
The formula for calculating the arc length of 144 is L = NR/ 180.
145 sector area formula: s sector =n r 2/360 = LR/2.
146 inner common tangent length =d-(R-r) outer common tangent length = d-(R+r)
Practical tools: common mathematical formulas
Formula classification formula expression
Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2)
a3-b3=(a-b(a2+ab+b2)
Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b
|a-b|≥|a|-|b| -|a|≤a≤|a|
The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
discriminant
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
The sum of the first n terms of some series
1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 13+23+33+43+53+63+…n3 = N2(n+ 1)2/4
12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Straight prism lateral area S=c*h Oblique prism lateral area S=c'*h Regular pyramid lateral area S= 1/2c*h'
Prism side area S = 1/2(c+c')h' frustum side area s =1/2 (c+c') l = pi (r+r) l.
The surface area of the ball is S=4pi*r2, and the side area of the cylinder is s = c * h = 2pi * h.
The lateral area of the cone is s =1/2 * c * l = pi * r * l.
The arc length formula l=a*r a is the radian number r > of the central angle; 0 sector formula s= 1/2*l*r
Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h
Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.
Cylinder volume formula V=s*h cylinder V=pi*r2h