**Established: January, 1958 an ARRL Affiliated Club since 1961**

**"Whiskey 8 Quack Quack Quack"**

**Meets at: James P. Capitan Center, Lower Level; 149 E. Corunna Ave.; Corunna, MI 48817** Monthly: 2nd Tuesday @ 7:00

Club station located in the James P. Capitan Center - Lower Level.

Grid Square EN72wx Latitude: 42.9819 N Longitude: -84.1164 W Alitude: 760 ft.

Shiawassee Amateur Radio Association presents some Science & Mathematics Reference Information which we hope is useful to viewers.

Using computers for mathematics leads quickly to "Spreadsheet" Programs. Using Windows, the first is Microsoft Excel, but that requirees a purchase. It is part of the Microsoft Office programs, so many have and use it. But if you want to go the free route, then there are some freeware spreadsheet programs we suggest you review. All are fully functional, free programs, so what do you have to lose?

This list is NOT all you can find, just a small sample. There are many 'free' spreadsheet programs for you to choose from. All operate on similar concepts, so pick one and dive on in. Note these are all 'Windows Based' products, Apple and Linux have ones available also --> just go a searching!

We have an Electronics Reference Page for basic Frequency & Wave Length; Capacitance & Inductance with Reactance; and Resonance basic information.

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 I added in 'Number' & 'Letter' sized drill bit table. I know I can quickly find the information it is handy any time - ** ENJOY**. Then the math work stuff really begins.

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 |

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 |

"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 |

'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' 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 'Built-in' Extensions Manager tool allows you to get access to hundreds official and third-party resources. Students and Engineers get a great tool for free!

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)

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)

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).

*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*]:

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 semi-major and semi-minor 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.

Where: *d* is diameter; *r* is radius; and 2*r = d*

Surface area [As] of a sphere:

Volume [V] of a sphere:

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:

NOTE: Some of the following equations can have two 'correct' solutions, so some **judgement is required !** Then the following results can be determined:

Most useful if you have any two sides and the included angle.

and rearrange to two other forms:

The law of tangents is most useful if you have two sides and an included angle or two angles and the included side.

In terms of: | |||
---|---|---|---|

Inverse functions are also called *"arc functions"*.

or

or

- Calculator Edge Site ~ Many types of online calculators.
- VK2ZAY Calculators ~ Many types of electronics calculators.

The Wolfram Language is a computer language and gives you a way to communicate with computers, in particular so you can tell them what to do. It is considered a "higher level" language to express to the computer what you want and then displays results back to you. As an aside, you may want to look up details on Mathematica {math solving software} and Wolfram Alpha {solution software} that are 'earlier' conceptual efforts on this process. Be advised that you should start with version 11 or higher if just beginning. Oh, lets mention that it runs on almost all operating systems - Windows, MAC, Linux, etc. (included on the RPi). On SARA's W8QQQ.org pages you will find some links to resources to get you going fast. Most probably you will need to 'signup' for a Wolfram ID along the way. It is pretty painless.

A powerful math tool is using "Wolfram Mathematica" for doing calculations and display. Many start out with the book "Hands-On Start to Wolfram Mathematica", 484 pages, by Cliff Hastings, Kevin Mischo, & Michael Morrison. The New Version 11 includes content for 3D printing and all the Version 11 graphics capabilities, including word clouds; customizing/labeling; and new content for working with data, audio, linguistic data and dates; and includes an all-new index. Publisher: Wolfram Media, Inc. (2016); ISBN: 9781579550127 (Paperback) [about $36.00] and includes website access. You can checkout Chapter 7 for free at: Wolfram Mathematica, Hands On, Chapter 7.

There is a companion video that goes through some concepts used in the book. uTube video on Wolfram Mathematics concepts.

There is free access to "An Elementary Introduction to the Wolfram Language" which works more like a reference guide than a series of tutorials, with each couple of pages outlining a concept or feature of Wolfram Language. The whole programming language is too vast to be covered in a single book, so it doesn't feature everything. Instead, it's more like edited highlights of concepts you really need to know. [Click the 'Read Online' Ribbon on the book cover.]

Then there is 'Wolfram U' which has training lectures and interactive courses that cover the language. Your first stop should be the full interactive course for the book "An Elementary Introduction to the Wolfram Language" that was listed in the previous paragraph by Stephen Wolfram.

Then try looking through some of these sites:

- Wolfram Resources (other) lists many sources on the web. ~ Wolfram Resources
- Wolfram Language Tutorial use a "bookmark" to keep this close as you work through the language. ~ Wolfram Language Tutorial.
- Mathematica Stackexchange is a community based exchange on various topics. ~ Mathematicia Stack Exchange.
- Fourier Theory & Applications in Wolfram Math. ~ Fourier Series Wolfram MathWorld ~
- Getting Started with Mathematica on RPi (uTube) ~ Introduction to Mathematica (RPi).
- Wolfram Fundamentals (uTube) by Prof. R.J. Gaylord's Wolfram Language Programming - 3 parts:

There are many other links for you to scan and use. Try searching the internet. Wolfram is very powerful language and it is 'free' on every RPi distribution over the last few years. Enjoy!

Electronics Reference Page from here you can get directly to the electronics reference page.

How we did it -- The equations shown on this page are presented by using *"Latex"* and the equation writing capabilities from the Code Cogs Web Site. Images are then stored "locally" to allow proper HTML5 validation.