Shiawassee Amateur Radio Association ~ W8QQQ
Whiskey 8 Quack Quack Quack
James P. Capitan Center, Lower Level; 149 E. Corunna Ave.; Corunna, MI 48817
Our ham station is located in Grid Square EN72wx at the EOC Center for James P. Capitan Center, Lower Level.
Latitude: 42.9819 N Longitude: 84.1164 W Alitude: 760 ft

Current Site Path: SARA HomeSARA's Reference Page SARA's Mathematics Reference
Page Navigation:
Decimal Equivalents
 Important Constants
 Formulas for Area
 Sphere Formulas
 Trig Formulas for Triangles
SARA's Science & Mathematics Reference Page
Shiawassee Amateur Radio Association presents some Science & Mathematics Reference Information which we hope is useful to viewers.
We have an Electronics Reference Page for basic Frequency & Wave Length; Capacitance & Inductance with Reactance; and Resonance basic information..
Decimal Equivalents (& Drill Sizes)
Not necessarily a math only issue but conversion of fractions of an inch to decimals (same value conversions as drill sizes). Seems like I am always looking for these and it takes me a long time (minutes) to find the information, so I put it here for my use! Works for both our purposes. Therefore the added in 'Number' & 'Letter' sized drill bit table. I can quickly know where the information is and quickly access any time  ENJOY. Then the work stuff begins.
Fractions & ANSI Size Drill Bit Selections
Fraction  Decimal  Fraction  Decimal  Fraction  Decimal  Fraction  Decimal 
(in.)  (in.)  (in.)  (in.)  
1/64  0.0156  17/64  0.2656  33/64  0.5156  49/64  0.7656 
1/32  0.0313  9/32  0.2812  17/32  0.5312  25/32  0.7812 
3/64  0.0469  19/64  0.2968  35/64  0.5469  51/64  0.7969 
1/16  0.0625  5/16  0.3125  9/16  0.5625  13/16  0.8125 
5/64  0.0781  21/64  0.3281  37/64  0.5781  53/64  0.8281 
3/32  0.0937  11/32  0.3437  19/32  0.5937  27/32  0.8437 
7/64  0.1093  23/64  0.3594  39/64  0.6094  55/64  0.8594 
1/8  0.0125  3/8  0.3750  5/8  0.6250  7/8  0.8750 
9/64  0.1406  25/64  0.3906  41/64  0.6406  57/64  0.8906 
5/32  0.1562  13/32  0.4062  21/32  0.6562  29/32  0.9062 
11/64  0.1719  27/64  0.4219  43/64  0.6719  59/64  0.9219 
3/16  0.1875  7/16  0.4375  11/16  0.6875  15/16  0.9375 
13/64  0.2031  29/64  0.4531  45/64  0.7031  61/64  0.9531 
7/32  0.2187  15/32  0.4687  23/32  0.7187  31/32  0.9687 
15/64  0.2344  31/64  0.4844  47/64  0.7344  63/64  0.9844 
1/4  0.2500  1/2  0.5000  3/4  0.7500  1  1.0000 
Numbered and Letter Size ANSI Drill Bit Chart
Decimal  Decimal  Decimal  Decimal  
Drill #  (in.)  Drill #  (in.)  Drill #  (in.)  Drill Letter  (in.) 
80  0.0135  53  0.0595  26  0.1470  A  0.2340 
79  0.0145  52  0.0635  25  0.1495  B  0.2380 
78  0.0160  51  0.0670  24  0.1520  C  0.2420 
77  0.0180  50  0.0700  23  0.1540  D  0.2460 
76  0.0200  49  0.0730  22  0.1570  E  0.2500 
75  0.0210  48  0.0760  21  0.1590  F  0.2570 
74  0.0210  47  0.0785  20  0.1610  G  0.2610 
73  0.0240  46  0.0810  19  0.1660  H  0.2660 
72  0.0250  45  0.0820  18  0.1695  I  0.2720 
71  0.0260  44  0.0860  17  0.1730  J  0.2770 
70  0.0280  43  0.0890  16  0.1770  K  0.2811 
69  0.0292  42  0.0935  15  0.1800  L  0.2900 
68  0.0310  41  0.0960  14  0.1820  M  0.2950 
67  0.0320  40  0.0980  13  0.1850  N  0.3020 
66  0.0330  39  0.0995  12  0.1890  O  0.3160 
65  0.0350  38  0.1015  11  0.1910  P  0.3230 
64  0.0360  37  0.1040  10  0.1935  Q  0.3320 
63  0.0370  36  0.1065  9  0.1960  R  0.3390 
62  0.0380  35  0.1100  8  0.1990  S  0.3480 
61  0.0390  34  0.1110  7  0.2010  T  0.3580 
60  0.0400  33  0.1130  6  0.2040  U  0.3680 
59  0.0410  32  0.1160  5  0.2055  V  0.3770 
58  0.0420  31  0.1200  4  0.2090  W  0.3860 
57  0.0430  30  0.1285  3  0.2130  X  0.3970 
56  0.0465  29  0.1360  2  0.2210  Y  0.4040 
55  0.0520  28  0.1405  1  0.2280  Z  0.4130 
54  0.0550  27  0.1440 
Some Important Constant Values
"Pi" is the ratio of Circumference to diameter for a circle.
Name  Symbol  Numeric Value 

Pi  3.14159265...  
Pi^2  9.86960440...  
Pi^.5  1.77245385...  
1/Pi  0.31830989...  
Pi/180  0.01745329...  
Pi/360  0.00872665...  
e  2.7182818...  
Degrees in 1 Radian  57.29577951...  
Radians in 1 degree  0.01745329...  
Speed of Light  c  299,792,458 m/sec or 
Speed of Light  c  983,571,056.4 ft/sec or 
Speed of Light  c  188,857.7297 mi/sec 
Newtonian Gravitational Constant  G  6.67384 x 10^11 m^3/(kg x sec^2) 
Plank constant  h  6.62606957 x 10^34 Jsec 
Coulomb's constant  8.98755178 x 10^9 Nm^2/C^2  
Wavelength  lamda or  c is 'Speed of Light' and f is frequency in Hertz (cycles per second) 
Characteristic Impedance of vacuum  376.73031346... Ohms 
Web Math Programs
Convert Units
'Convert for Windows' is a very useful free program to convert from one value of measurement into another type of unit. It covers: Force; Light; Mass; Power; Pressure; Speed (velocity); temperature; Time; Volume; Volume  Dry; Accelleration; Angle; Area; Density; Distance and Flow. Also, a 'custom' area allows you to enter your own conversions (if required by you... example money conversions). Convert for Windows Freeware Program
SMath Studio
'SMath Studio' is a free math studio for entering math equations and doing ploting, design, and other mathematical investigations in topics of your choosing. SMath Studio Tiny, powerful, free mathematical program with WYSIWYG editor and complete units of measurements support. It provides numerous computing features and rich user interface. The application also contains integrated mathematical reference book. A 'Builtin' Extensions Manager tool allows you to get access to hundreds official and thirdparty resources. Students and Engineers get a great tool for free!
Formulas for Area
Rectangle ~ Area (Straight Sides)
The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length (l) and width (w), the formula for the rectangle's area is:
A = l w (rectangle)
That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w which is a square, the area of a square with side length s is given by the formula:
A = s ^{2} (square)
Triangle ~ Area
It follows that a triangle's area is shown to be one half the area of a rectangle (or parallelogram), namely: {b is base and h is height}
A = 1 (b * H) / 2 (triangle)
Dissection of parallelograms into triangles
Many simple formulas for area follow from the method of dissection. This involves cutting a shape into pieces, whose areas must be summed to attain the area of the original shape.
For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in the figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure becomes a basic rectangle. It follows that the area of any parallelogram has the same formula (thus same area) as a rectangle with same width and height.(area is just the product of the length and width).
A = l w (parallelogram)
However, the same parallelogram can be cut along one of the diagonals into two congruent triangles, as shown in the figure to the right. Each triangle has height, h, and width, b. You can use the triangle area formula to find the area of one triangle, and then multiply by 2 (two triangles) to get the parallelpgram's area.
It is easy to see that the area of each triangle is half the area of the parallelogram:
A = 1 (b * H) / 2 (triangle)
Similar arguments and methods can be used to find area formulas for any trapezoid, as well as many more complicated polygons. If one tries the method of dissection and looking at results, usually the correct formula can be found. The polygon's area will be the sum of all the areas from each of the small divisions summed up. As you do these disections, triangles and the ability to work with them becomes important. This leads to the field of "Trigonometry" (see below).
Circle ~ Area & Parts (Curved Sides)
A = Pi r^2 (Circle with Radius, r) or A = Pi d^2 / 4 (Circle with diameter, d)
The formula for the area of a circle can be based on a similar method as used in parallelograms above. Given a circle of radius r (a disk), it is possible to partition the circle into sectors, as shown in the figure to the left. Each sector is approximately triangular in shape, and the sectors can be rearranged to form an approximate parallelogram. The height of this parallelogram is r, and the width is half the circumference of the circle, or (Pi)r. Thus, the total area of the circle is r x (Pi r), or Pi r^2, as 2r = d the formula can be rewritten as Pi d^2 / 4
The side [s] of an inscribed square becomes:
or
Length of an arc (small curved piece of the circle) becomes: [L ]:
or
Area of a sector [A s]:
List of Common Formulas for Area
Shape  Formula for Area  Variables 

Regular Equilateral Triangle  s is the length of one side of the triangle.  
Triangle 1  s is half the perimeter, a, b and c are the length of each side.  
Triangle 2  a and b are any two sides, and C is the angle between them.  
Triangle 3  a and h are the base and altitude (measured perpendicular to the base).  
Isosceles triangle  a is the length of one of the two equal sides and b is the length of the different side.  
Rhombus/Kite  a and b are the lengths of the two diagonals of the rhombus or kite.  
Parallelogram  b is the length of the base and h is the perpendicular height.  
Trapezoid  a and b are the parallel sides and h the distance (height) between the parallels.  
Regular hexagon  s is the length of one side of the hexagon.  
Regular octagon  s is the length of one side of the octagon.  
Regular polygon 1  l is the side length and n is the number of sides.  
Regular polygon 2  p is the perimeter and n is the number of sides.  
Regular polygon 3  R is the radius of a circumscribed circle, r is the radius of an inscribed circle, and n is the number of sides.  
Regular polygon 4  n is the number of sides, b is the side length, a is the apothem, or the radius of an inscribed circle in the polygon, and p is the perimeter of the polygon.  
Circle  r is the radius and d the diameter.  
Circular sector  r and theta are the radius and angle (in radians), respectively and L is the length of the perimeter.  
Ellipse  a and b are the semimajor and semiminor axes.  
Total surface area of a cylinder  r and h are the radius and height.  
Lateral surface area of a cylinder  r and h are the radius and height.  
Total surface area of a sphere  r and d are the radius and diameter.  
Total surface area of a pyramid  B is the base area, p is the base perimeter and L is the slant height.  
Square to circular area conversion  A is the area of the square in square units.  
Circular to square area conversion  C is the area of the circle in circular units. 
The above calculations show how to find the areas of many common shapes. Hope they help you.
Sphere Formulas (Area & Volume)
Where: d is diameter; r is radius; and 2r = d
Surface area [As] of a sphere:
Volume [V] of a sphere:
Trigonometry Formulas for Triangles
Trigonometry is the mathematical branch dealing with relationships of sides and angles in triangles. It also deals with a "unit vector" rotating around a point of origin, which has an angle of rotation, a unit vector and the 'x axis' and 'y axis' values for the vector's end pont (a triangle with sides, 'x', 'y'; hypotenuse ~ 'c' and the rotational angle {theta}).
In triangle terms:
In 'unit circle' terms:
Also defined is the reciprocal of each function:
Given a triangle with angles A, B, and C that are respectively opposite the sides a, b, and c.
NOTE: Some of the following equations can have two 'correct' solutions, so some judgement is required ! Then the following results can be determined:
"Law of Sines"
"Law of Cosines"
Most useful if you have any two sides and the included angle.
and rearrange to two other forms:
"Law of Tangents"
The law of tangents is most useful if you have two sides and an included angle or two angles and the included side.
Trigonometry functions expressed in terms of the other basic trigonometry functions:
In terms of:  

Inverse Functions
Inverse functions are also called "arc functions".
or
or
You can get to the electronics reference page ~ Electronics Reference Page from here.
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Page Navigation:
Decimal Equivalents
 Important Constants
 Formulas for Area
 Sphere Formulas
 Trig Formulas for Triangles
Web Site Contact: W8QQQ at arrl.net
Page Last Updated: 04Sep2018
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