This website approximately 85% completed, and it contains 9396 words, and a hyperlinked table of contents. The material in this e-book still requires some editing. Some additional text will also be added before it is completed.
Created by David@TechForText.com 2010©
Each topic is written as an independent article, with the assumption that the reader may not have read previous topics in this e-book. Thus, relevant information may be repeated in some of the topics. All of the topics are written primarily for individuals with relatively advanced backgrounds in mathematics and spreadsheet software. This is because creating calculation devices is an advanced topic, involving a type of computer programming with mathematical concepts.
Links to websites, created by other authors, are provided in this e-book,, for additional information and resources, and a diverse perspective on spreadsheets, mathematics, and calculation devices. This includes links for instructional videos, and various types of free software available for download.
THE HYPERLINK TABLE OF CONTENTS OF THIS WEBSITE
Left click with the mouse, on the upper portion of the blue
words that relate to the topic or subtopic you are interested in.
Internet Explorer http://www.microsoft.com/windows/internet-explorer/
Google Chrome http://www.google.com/chrome/
The calculation devices that I created in the spreadsheet format require Microsoft Excel, or the OpenOffice.org software package, and the Windows operating system. If you do not have Microsoft Excel, you should download the OpenOffice.org software package, because it is free. This software package is almost as good as Microsoft Office, and it contains spreadsheet software (OpenOffice Calc) that has most of the functionality of Microsoft Excel.
Incidentally, highly complex calculation devices, involving thousands of formulas, may require a relatively powerful computer, to function optimally. However, the most complex devices created for this website involve less than 150 formulas.
Based on the way I am using the terminology, dedicated calculation devices are software based devices that are designed to carry out a specific type, category or set of calculations. The dedicated devices are very different than conventional mathematics software that can perform many types of calculations, such as conventional spreadsheets, the Windows calculator, MathCAD, Mathematica, etc.
However, dedicated calculation devices, have some unique advantages over conventional mathematics software. This includes practical utility that can only be obtained from dedicated calculation devices. This is explained in the following paragraphs.
There are several very important uses and advantages that dedicated calculation devices have over conventional mathematics software, which include the following:
1) Dedicated calculation devices can be created to perform a large number of calculations simultaneously, when the same input data applies to a set of calculations. This can involve dozens, hundreds, or even thousands of calculations performed simultaneously, by one specially designed calculation device. This can save time and work, and money for business. With a large set of highly complex calculations that are frequently carried out, several weeks of work might be saved each year.
2) Dedicated calculation devices are usually very user-friendly. These devices can be designed for users without mathematical backgrounds, (such as clerks, and administrative assistants) so that they can perform very complex calculations, just by entering data and clicking with the mouse. This can give managers the ability to obtain complex mathematical feedback, with out delay and with out waiting for the assistance of mathematicians. This also can save time and work, and the expense of hiring experts to carry out complex calculations that are frequently performed.
3) Dedicated calculation devices can be designed for advertising and sales. This can involve calculation devices that function over the Internet that relate to the potential cost of products or services. Examples are calculation devices that calculate the cost of loans, and mortgage versus rent. Especially useful for sales over the Internet are calculation devices with submit buttons. These devices add up the total cost of the items the customer enters. Then the customer finalizes the purchase by entering a credit card number, and pressing a submit button.
Dedicated calculation devices are time consuming to create, and they must be designed for a specific type, category or set of calculations. Thus, creating these devices is only practical when the same type of calculation is required on a regular basis. If this is not the case, using conventional mathematics software, such as spreadsheets, MathCAD, or even a hand held calculator is the best option, unless you can find a dedicated calculation device that already exists.
There are many dedicated calculation devices on the Internet, especially for commonly performed calculations. Some of these devices I have created myself, and they are listed at www.TechForText.com/Math. You can find calculation devices on the Internet created by many other authors by using the search phrase that relates to the calculations you want to perform. This is of course a trial and error type of search. For common mathematical problems, you will probably find an appropriate online dedicated calculation device on the Internet.
However, for highly unusual or highly specialized calculations the best option for an individual is to use a hand-held calculator, or conventional mathematics software. The best option for a large or medium-size business is to hire someone to create the required dedicated calculation device.
Almost any programming language can be used to create dedicated calculation devices. However, writing computer code for these devices can be very time-consuming. Some of the devices I have created have hundreds or even thousands of lines of code. One of the devices that I created had 82 pages of computer code. It can take many days, weeks, or even months to create these devices by writing code.
However, I DO NOT create calculation devices by writing conventional computer code. I create them using spreadsheet software, but these devices generally do not look like or function like conventional spreadsheets. They have clearly delineated input boxes for data, and clearly defined sections for the calculated results. They are designed so that data can only be entered in the input boxes, and the calculated results are presented in relatively large display boxes. Just like conventional software, these calculation devices can be reused indefinitely, and they are not consumed like a conventional spreadsheet. However, they cannot operate without the spreadsheet software that was used to create them, and they cannot function over the Internet.
After the conversion process is completed, it is usually necessary to slightly edit the resulting computer code, in an HTML editor, to maximize functionality and aesthetics of the calculation device. After this editing process is complete, I usually copy the code and paste it into a webpage I design for the device.
The first technique involves using cell designations to represent the letters in conventional equations and formulas. The second technique involves renaming cells with the letters in the equations and formulas. (That is the default cell designations are replaced with the letters in the equations and formulas.) With both of these techniques, it is necessary to write algebraic equations in terms of letters. Then the equations can be solved for the unknowns in terms of letters. This results in formulas for the unknowns. These formulas must be converted to spreadsheet formulas, using the techniques explained in the following subtopics.
Note: Another method of creating calculation devices involves using the Goal Seek mechanism available in Microsoft Excel, OpenOffice Calc, and probably some other brands of spreadsheet software. With the Goal Seek mechanism the spreadsheet software solves equations, using a type of trial and error process. This is especially useful for algebraic equations that cannot be solved with conventional techniques, or equations that are time consuming or difficult to solve with conventional methods. However, to use the Goal Seek mechanism it is necessary to convert algebraic equations into a format that can be used in a spreadsheet. This can be done with either of the techniques mentioned above.
Using cells to represent variables is one of the most practical ways of creating calculation devices. It can be useful for all types of calculations, including algebra. This method is described below in a step-by-step way.
The first step involves solving an equation that relates to the calculation device that you want to create. This equation should be general enough to define the set of equations you want to solve. I will use the following simple equation as an example: AX+BX+CX =N. Keep in mind that this equation represents a set of many equations, (an infinite set) where the letters A, B, C and N can have many different values. For example, all of the following equations belong to the set:
(when A=0) 3X+9X =36,
(when A and B=0) 10X =1000,
This equation AX+BX+CX=N can easily be solved for X. as follows X(A+B+C)=N, and then X=N/(A+B+C) The result for X, highlighted in yellow, can be used as a spreadsheet formula, with the modifications described below.
The next step, with this method, is to use the cells in a spreadsheet to represent the values of A, B, C, and N. We can actually use any set of cells we choose, but for convenience, I will use the following:
A=cell D11 ,
B= cell D12,
C= cell D13
N= cell D14
The next step is to write the results of the equation we solved above X=N/(A+B+C) in terms of the above cells. When this is done we have X=D14/(D11+D12+D13). Now we must assign a cell to represent the calculated result for X. I will use cell D16=X. The formula we derived above (X=D14/(D11+D12+D13) provides the calculated value of X. If we place the formula =D14/(D11+D12+D13) in cell D16, for example, the D16 will display the calculated value of X. Note the letter X is not part of the formula that is put into cell D16, and the same applies to A, B, C, N.
With the method that I am describing here, the spreadsheet cannot recognize the meaning or value of letters. However, it is necessary to place the letters A, B, C, N, and X next to the cells that we used to represent them, so that the user will know where to enter the numbers, and where to find the value of X. The most convenient place is to put these letters to the *left of the numbers within an equal sign, as follows:
A= is placed in cell C11 because we used cell D11 to represent A
B= is placed in cell C12 because we used cell D12 to represent B
C= is placed in cell C13 because we used cell D13 to represent C
N= is placed in cell C14 because we used cell D14 to represent N
X= is placed in cell C16 because we used cell D16 for the calculated result which is the value of X.
*NOTE, the above input boxes can be labeled many other ways, such as by placing the letters A, B, K, N, on top of the input box. When an input box is labeled with a word, I often place the label on top, or sometimes on the bottom of the input box.
The technique described above, is probably the simplest way of creating a calculation device. However, this method has some disadvantages. Rewriting formulas in terms of cell designations can result in errors, and it can be tedious when a formula has many terms. It is also difficult to explain a formula written in terms of cell designations to others, because each term has a letter and number. For example, 6+Y can be rewritten for a spreadsheet as 6+ D10, and it can be misinterpreted by a person as 6+ 10 times D. All of these difficulties can be eliminated with the technique described in the following subtopic.
The first two or three steps with this technique are the same as the alternative method described above. That is, write an equation that you want to solve, in terms of letters. Then, solve the equation for the unknown.
I am using the same equation that I used in the previous subtopic as an example, but I am replacing the letter C with K, because of technical reasons. When this equation AX+BX+KX=N is solved for the unknown, X, the result is X=N/(A+B+K).
The next step is to choose a set of cells on the spreadsheet to serve as input boxes, where the user will enter the values of: A, B, K, and N. (For this example, I am using Cell B2, Cell B3, Cell B4, and Cell B5.) The input boxes should be labeled by placing the appropriate letter, with an equal sign, to the *left of the input boxes, such as:
A=[Input Box Cell B2]
B=[Input Box Cell B3]
K=[Input Box Cell B4]
N=[Input Box Cell B5]
*NOTE, the above input boxes can be labeled many other ways, such as by placing the letters A, B, K, N, on top of the input box. When an input box is labeled with a word, I often place the label on top, or sometimes on the bottom of the input box.
Here is the difference between this technique, and the method described in the previous subtopic. After the above has been completed, the variables A, B, K, and N are defined in terms of the input boxes shown above. This simply means that the four cells (B2, B3, B4, B5) are renamed to: A, B, K, and N. This renaming technique is done with a mechanism designed for the purpose, which is available in Microsoft Word, OpenOffice Calc, and some other brands of spreadsheet software.
Specifically, the four cells are renamed as shown below, which results in the indicated relationships between the cells and letters.
Cell B2 is renamed to A As a result of this renaming: wherever =A is placed on the spreadsheet, it will display the number or letters that the user enters in Cell B2.
Cell B3 is renamed to B As a result of this renaming: wherever =B is placed on the spreadsheet it will display the number or letters that the user enters in Cell B3.
Cell B4 is renamed to K As a result of this renaming: wherever =K is placed on the spreadsheet it will display the number or letters that the user enters in Cell B4.
Cell B5 is renamed to N As a result of this renaming: wherever =N is placed on the spreadsheet it will display the number or letters that the user enters in Cell B5.
For example, if the number 5 is entered in cell B2, which is the input box for A, A would be equal to five. If A was multiplied by 2, such as =2*A, and placed in any cell on the spreadsheet, the result would be 10.
Now, we can return to the equation that was obtained by solving AX+BX+KX=N for X, which is: X=N/(A+B+K). This equation, highlighted in yellow, now can be used as a spreadsheet formula, assuming that the cells indicated above were appropriately renamed. This simply involves removing the X. and placing the formula =N/(A+B+K) in a convenient cell on the spreadsheet. For example, if we place =N/(A+B+K) in cell B6, B6 will display the calculated results. We can also rename cell B6 to X.
Renaming cells that display calculated results, with an appropriate letter, or word, can be quite useful. It can prevent confusion and errors when the calculated results must be transmitted to other formulas, or to error-checking devices, which are discussed in the next topic.
The two methods discussed in the previous subtopics, for creating calculation devices using conventional formulas are both quite useful. Both of these methods can be used on the same spreadsheet, to make a calculation device.
Generally, renaming cells to match letters in formulas is usually the most efficient technique. It reduces the chances of making errors when creating a complex calculation device. If there is an error, it may be easier to spot the difficulty, when cells have been renamed to match the letters in formulas.
However, there are situations where the alternative technique is easier and more efficient, which is using cell designations to represent the letters in formulas. One of these situations is where many copies of the same formula are required all the way down a column, or cross a row. This is illustrated in the following example:
Let us assume we need 100 copies of the formula 2X=N, all the way down a column, with 100 input cells, and 100 display cells. We can write this formula (2X=N) in terms of cell designations as =2*A1. (If we put this formula in cell B1, cell A1 will be the input box, and cell B1 will be the display cell. That is whatever number is put in cell A1 will be multiplied by two, and displayed in cell B1. ) To make the 100 copies of the formula we can use the following technique:
The four steps above will produce 100 formulas, each with its own input cell, and display cell. There is a slightly different alternative method that can do the job just as well various, listed below:
Another situation using the default cell designations may be preferable, for some people, is when the calculation devices involves one or two formulas, or when you are entering the default formulas provided with the spreadsheet software. This technique might save a little time, and complexity, for some people, because it eliminates the step of renaming spreadsheet cells.
If you are making conventional spreadsheets, such as for addition, subtraction, percentages, there is usually no reason to rename cells. This is especially the case if you are using default spreadsheet formulas, from the toolbar.
When a calculation device has been completed, it is usually not relevant which of the two techniques were used to create it. The level of utility and functionality of a properly designed calculation device is not determined by the technique that was used to create it. This can be seen in the next two subtopics.
If you want a calculation device that was created by Substituting Cell Designations for the letters in the equation: AX+BX+CX=N, left click on one or more of the following links. (All of the following calculation devices solve the equation: AX+BX+CX=N, for X.):
If you want calculation devices created by renaming spreadsheet cells to match the letters in AX+BX+KX=N left click on one or more of the following blue hyperlinks. (All of the following calculation devices solve the equation: AX+BX+KX=N, for X.):
If you want the above calculation device (created by Defining Variables in Terms of Cell Designations) in the newer 2007 version of Microsoft Excel, left click on these words for downloading. This requires the 2007 version of Excel.
Error-checking devices, based on the way I am using the terminology in this text, are mechanisms that are incorporated into a calculation device that checks calculations for errors, or evaluates the accuracy of calculations. The error-checking devices may display text that indicates if there are errors in the calculation, such as Error, or No Error. Some of these devices display numbers, indicating the relative degree of error or accuracy. This can involve the display of the degree of error or accuracy in percentage, such as 0% error, or accuracy 100%.
The simplest error-checking devices display two numbers in separate display boxes. One number represents the left side of an equation, and the other the right side. If the numbers in both display boxes are equal there are no errors. If the numbers in the display boxes are not equal there are errors. A similar device, calculate the difference between the left and right side, by subtraction. If the result is zero there are no errors, but if the results is less than or greater than zero there are errors.
The error checking devices can detect if malfunctions, in hardware, software, or the calculation device itself are causing calculation errors. Errors of this type are relatively rare. Sometimes a calculation device can become corrupt, over time. This can occasionally happen if the user inadvertently deletes a formula. However, this is usually not a possibility, because most well-made calculation devices have
If the fault error-checking does not display an error message. That is there are default mechanism built into spreadsheet software that may display errors message when numbers do not satisfy an equation, IN SOME CASES. For example, if the user entered numbers that result in division by zero, you will see a fault error message.
The error checking device can spot mathematical errors while a calculation device is under construction, and after it has been completed. This can save a considerable amount of time and effort, when creating complex calculation devices, especially if there are many formulas, and/or formulas that have many terms.
This device might also spot certain types of software and computer malfunctions that result in calculation errors, which are extremely rare.
If there are errors that relate to the way the letters in the formula were defined, with the name mechanism, you will see the default error message in Microsoft Word or OpenOffice Calc, which is #NAME?
We can expand the utility of the principles, and technique described in the subtopic presented above to create an error checking device. The additional utility becomes apparent when we rename cell B6 to X. Keep in mind that with our example, cell B6 contains the formula that calculates the value for X, which is the formula highlighted in yellow =N/(A+B+K). Thus, with this example, the value for X is displayed in cell B6.
If we place this equation without the N, =A*X+B*X+K*X in any cell on the spreadsheet, the value of N will be calculated, and displayed. If we place =N in any cell on the spreadsheet the value the user entered for N will be accessed, and displayed. If there are no errors the two values will be equal. That is the calculated value for N will equal the value the user entered for N. In general, the left side and right side of an equation must be equal. With our example, the left side is (A*X+B*X+K*X) and right side is (N).
The simple error checking device described above can save time when creating a calculation device. This is especially the case, when a calculation device requires a large number of complex equations, which must be converted to spreadsheet formulas. The error checking device quickly checks formulas. For example, if the equation =A*X+B*X+K*X=N was incorrectly solved for X, such as =N/(B+K) the word FALSE will appear in the cell that contains the equation: =A*X+B*X+K*X=N. If the correct formula was entered, which is: =N/(A+B+K), you will see the word TRUE.
The simple error checking device scribed above sometime display error messages, when there are no errors. This can happen when the calculations are complex, especially if the numbers have many digits. This happens as a result of rounding errors, which are usually not significant. For example, FALSE will be displayed, indicating an error, if the user enters 10 for N, and the calculated value for N is A*X+B*X+K*X=9.999999999999. This difficulty can be eliminated by using the ROUND function, set to five or six decimal places, as shown below:
=ROUND(A*X+B*X+K*X, 5)=ROUND(N, 5)
Note the concepts discussed in the following paragraphs applies to Microsoft Excel, OpenOffice Calc, and other advanced spreadsheet software. There are brands of less complex spreadsheet software available, which may not have the versatility and functionality that are discussed in the following paragraphs.
A concept that can be useful for developing creative skills with spreadsheet software is to realize you are dealing with a computer language that is based on mathematics and *symbolic logic. I will call this the spreadsheet computer language. If you are entering a few formulas, from the toolbar, or creating a conventional spreadsheet, the concept of a computer language is not apparent, and not even relevant. However, when creating complex calculation devices, with sets of formulas that interact with each other in complex ways, it is helpful to understand the mathematics, logic and notation of spreadsheets as a computer language.
Statements created with Spreadsheet functions for symbolic logic, resemble computer code
*The symbolic logic consists of logical statements written in an abbreviated form with spreadsheet functions, such as =IF( ) =AND(), =OR(). This also includes any statement that can be defined as true or false, such as =A=B, =C<D, and =P>G. The symbolic logic can involve long statements involving a number of spreadsheet functions, conventional formulas modified for spreadsheet use, logical statements that define a set of numbers, as well as text. All of this certainly resembles computer code, and it is feasible to write a series of statements with this code that can perform many operations, including the following:
Evaluate calculated results, for accuracy, or inaccuracy, and display related text
Display specified text when a predefined condition exists. For example, a device that calculates money, indication wither or no
Channel numbers or text through various pathways to one or more cells, based on specified criteria. For example, sending even numbers to a set of spreadsheet cells on the left, and odd numbers to a set of spreadsheet cells on the right.
The type of calculations carried out on a set of numbers, can be controlled and written statements entered by the user.
Spreadsheet formulas Formulas also often look like computer code in complex calculation devices. This is especially the case when formulas are lengthy, or when many formulas are connected in complex configurations, to obtain a calculated result.
The formatting code is also essentially a type of computer code. (This is probably only familiar to very advanced spreadsheet users.) The formatting code controls how numbers and letters are interpreted and displayed on a spreadsheet. Numbers can be interpreted and displayed on a spreadsheet as a day, a month, a specific date, a time, a conventional number, scientific notation, a percentage, a fraction, as dollars, etc. For example, 1 can mean any of the following depending on the formatting code”
Sunday (the code is dddd)
January, (the code is mmmm)
January 1, 1900, (the code is mmmm d, YYY)
100% (the code is 0.00%)
$1.00 (the code is $#,##0.00)
1 (the code is General).
The spreadsheet computer language provides ways to create connections between input cells (where the user enters numbers), output cells (which display calculated results), and formulas. When using spreadsheet software in a conventional way, most of us probably do not think of creating connections between any of the above. However, when creating complex calculation devices, it is necessary to devise precise connections between input and output cells and formulas. This often involves very complex configurations, involving hundreds of connections, from input cells, to formulas, which may transmit their calculated results through connections to many other formulas. This is the case with the Multiple-Algebraic Calculator.
I have not come across any sources that called the above a computer a language. However, the notation, symbolic logic, the compact nature of formulas and formatting code, and a number of other aspects associated with spreadsheets, fit the definition of a higher-level computer language. It also provides the versatility of a computer language, which is probably not apparent to most people that use spreadsheets.
Most of the spreadsheet formulas I used to create the multiple algebraic calculator, I created by solving conventional equations, for the variable I needed. This essentially results in a conventional formula, which cannot be used in spreadsheets. I then converted these formulas into spreadsheet formulas by making a few modifications. This included using an asterisk (*) for multiplication, slashes (/) for division, and a carrot (^) with an appropriate number for square roots, cube roots, squares, etc. However, the resulting formulas required further modification, because they contained letters that spreadsheet software CANNOT identify, in mathematical terms.
There are two basic ways to make the letters in a conventional formula meaningful to spreadsheet software. One method involves the use of cell designations, which are the default names of spreadsheet cells, based on the way I am using the terminology. Three examples of cell designations are, A5, B3, and G9. Cell designations are also called cell references.
The basic technique of converting a conventional formula to a spreadsheet formula is to replace the letters in the formula with relevant cell designations. (This must be coupled with the modifications discussed in the previous subtopic.) The relevant cells are usually the input cells where the user enters numbers for the formula. Sometimes relevant cells are cells that contain calculated results from other formulas.
Conventional formulas that have been rewritten with cell designations can be confusing to work with, and even more confusing when they are presented to other people for study. The alternative to this technique is to define the letters in a formula in terms of cell designations. This essentially involves renaming the cells on the spreadsheet to match the letters in the formula. There is a mechanism in Microsoft Word, and OpenOffice Calc that provides this functionality. With this technique the letters in the formula are not changed.
For illustration purposes I will use a simple formula for area, which is length multiplied by width equals the area. This formula can be represented as L*W=A. Now if we want to convert this into a spreadsheet formula, we must use two input cells, one for the user to enter the length and the other for the width. For this example let us assume we are using cell B3 for length, and cell B4 for width. With the first technique described above, the area formula must be rewritten in terms of cell designations, which in this case is =B3*B4. Let us assume we are placing this formula in cell B10, which will display the calculated results.
With the alternative method described above, cell B3 is renamed to cell L, and cell B4 is renamed to cell W, and the letters in the formula are not changed, but the equal sign is always placed on the left side, as such: =L*W. If we place this formula in cell B10, our calculated results will be displayed in cell B10.
Cell B10 can also be renamed if necessary, which can involve a letter, such as A, or even a word such as area. This renaming would make it quite easy to transfer the calculated results to another formula. This is explained in more detail in the following topic.
If several formulas are placed on a spreadsheet, they will not result in a calculation device that performs multiple calculations simultaneously. The formulas must be connected to each other in a logical configuration. This generally involves creating a structure where the output (calculated result) of one formula, is fed into one or more other formulas. This is similar to connecting electronic components to each other on a circuit board. The connections lead from one component to another in predetermined pathways through wires. With spreadsheet formulas there are no wires, but we can think of the connections as virtual wires, or imaginary wires. However, the important idea to understand is the connections between formulas are real.
Note, sometimes it is convenient to replace the default cell designations, with names, such as a letter or word. When this is the case, the names can be used in the same way that the cell designations are used to connect a series of formulas in a chain like sequence. Keep in mind that cell designations are actually the default names. If a cell is renamed A, B, area, time, mass, money, taxes, or payroll, all of the techniques, principles, and examples that apply to the cell designations also apply to the renamed cells.
When formulas are connected in a chain like configuration as described above, the calculated result of the first formula in the chain is needed to calculate the second result. The third result cannot be calculated until the second result has been calculated. This sequence continues throughout the chain. Thus, when formulas are connected in the chain configuration, the computer must calculate the results in sequence. That is it must calculate the result from the first formula in the chain, then the result from the second formula, followed by the third, fourth, fifth, etc.
Generally a sequential chain of calculations involving a number of formulas, are carried out at a very rapid rate, and from the perception of the user, all the calculations appear to be calculated simultaneously. I use the words simultaneously or simultaneous from the perception of the user in this text, unless otherwise noted.
A sequential chain of formulas on a spreadsheet is not the only configuration that will result in multiple calculations that are carried out simultaneously. This is explained in the next subsection.
One or more input cells can be connected to many formulas for multiple and simultaneous calculations. For example, let us assume that A3 and A4 are input cells. When the user enters numbers in A3 and A4, and presses the enter key, all of the following formulas will calculate results simultaneously. With this example, all the results are determined by the numbers entered into cells A3 and A4:
I am continuing with the above example. If we have spreadsheet formulas that have additional input sources, besides cells A3 and A4, they will also be calculated simultaneously, but there calculated results will not be totally determined by the numbers in cells A3 and A4. The following set of formulas is an example:
=B2*A3*A4, =C4+A3+A4, =(C5+A3)^A4, =B3/A4, =(B2+A3)^2, =(C2+A3)^3, =2*B7*A3, =2*B4+A3,
With the examples presented above, the spreadsheet formulas were connected to input cells, where the user enters numbers. However, the above configuration, or something similar to it, can involve a number of formulas that are connected to one or more formulas. That is in stead of input cells, the above formulas could have been connected to the calculated results from one or more other formulas. This concept is important for creating complex calculation devices, which often require many formulas connected to each other in complex configurations.
The spreadsheet formula connections (discussed above, in three subtopics) are similar to the series and parallel connections in electronics. See the following websites for information on this concept from the prospective of electronics:
The first technique described above, (connecting formulas in a chain like sequence) is similar to electronic components connected in series. When electronic components are connected in this way, the electric current flows from one component to another, and if one component fails, it will affect the entire circuit. The same applies to a malfunctioning spreadsheet formula connected in this type of configuration. Small Christmas tree lights are often connected in series, on a long wire, and if one light malfunctions, it will cause the entire string of lights to malfunction.
The second method discussed above, involved connecting spreadsheet formulas to the same data source. The simplest example of this type of connection is one or more formulas connected directly to a set of input cells. This is similar to connecting electronic components in parallel. Parallel connections are essentially independent from other electronic components on the circuit. For example, the lighting circuits used in homes and business establishments are generally connected in parallel. If one light bulb malfunctions, it will not affect other light bulbs on the circuit. The same applies to spreadsheet formulas that are connected in parallel. If one formula fails, it will not affect the calculated results of other formulas, assuming that the connections truly fit the parallel configuration.
With both spreadsheet formulas and electronic components, the connections needed to create a complex device usually involve both series and parallel configurations. This can consist of a number of components connected in series, which branch off to one or more parallel connections. A parallel connection can also branch off to one or more sets of components that are connected in series. The out put of two or more connections are sometimes channeled into one component. For example, the calculated results of a number of formulas can be channeled into one formula for additional calculations. This can involve calculating the sum of several calculated results.
Words on website: University of Akron This is the review of Algebra in 10 lessons http://www.math.uakron.edu/~dpstory/mpt_home.html
This essentially a free review course on algebra, and it is provided in the PDF format.
Words on website: financial accounting
This is an e-book on accounting
List of Websites for spreadsheets
words of website:\\
Words on website: A video instructional series on statistics for college and high school classrooms and adult learners; 26 half-hour video programs and coordinated books http://www.learner.org/resources/series65.html#