Microsoft Excel as a Programming Language,
To Create Databases and Complex Calculation Devices

 

Created by David Alderoty © 2012

 

To contact the author use: David@TechForText.com or

left click on the link below for a website communication form.

Link for a Website Communication Form

 

 

Introductory Concepts

This website demonstrates how Microsoft Excel can be used as a programming language, to create databases and complex calculation devices that carry out SETS of calculation simultaneously.  However, this text does NOT provide detailed instructions on how to create software.  Specifically, it is a demonstration with software I created, in the summer of 2012, with Microsoft Excel, coupled with descriptions of a few of the concepts and techniques I use when creating software. 

            The software I created with Excel is UNLIKE conventional spreadsheets, and many of these devices function over the Internet, in conventional web browsers.  This software performs complex sets of calculations involving. 1)Algebra with Hyperbolic Functions,  2)Calculus with Hyperbolic Integrals,  3)Calculus with Triple Integrals, 4) Trigonometry.  This also includes 5) Databases with Calculation Mechanisms, such as for counting the number of entries in the database, and for statistical calculations.

            This software is provided free of charge, and you can download the software with the links on this webpage, or from the related websites presented below.  This software is available in a Microsoft Word and/or JavaScript format.  However, the databases are available only in the Excel format.  The Excel devices require Microsoft Windows and Excel 2003, 2007, 2010, or later versions.  The JavaScript software should operate with most web browsers and operating systems, but they were only tested with Windows.

 

 

How Microsoft Excel Can Be Used As A Programming Language

Creating complex software with Microsoft Excel is NOT the same process as creating conventional spreadsheets, by inserting Excelís default functions, by clicking on menu icons.  This will become understandable with the following explanations, and examining of the online JavaScript software I created with Microsoft Excel. 

            When software is created with Microsoft Excel, the code is comprised of spreadsheet formulas, formatting code, input cells, output cells that display results and storage cells that store formulas and/or text messages.  All of the above must essentially be wired together, in various types of parallel and serial configurations, similar to the way electronic circuits are created.  Of course, the wires connecting one component to another are mental conceptualizations that represent the flow of data from input cells, storage cells, formulas, and outputs cells.  This often involves one formula transmitting its calculated results to a number of other formulas for additional calculations.

            When creating complex software, most of the spreadsheet formulas must be created by cognitively translating conventional mathematics and logical operations, into a format that can be used in Excel.  For example, if you want to create software that displays the step-by-step solution to an algebraic equation, generated with numbers entered by the user, you must create a set of formulas that display each step.  This is illustrated below, with four spreadsheet formulas that I created, to display the step by step solution to a simple algebraic problem, such as: BX+C=D, or 3X+112 = 5460.  With the spreadsheet formulas below, Digit6, H, F, and A are the names of cells which TRANSMIT NUMBERS to the set of formulas.

 

=(1+Digit6)&"X+"&H&" = "&F*A

=(1+Digit6)&"X="&F*A&"-"&H

=(1+Digit6)&"X="&F*A-H

="X="&(F*A-H)/(1+Digit6)

 

            Thus, you CANNOT create complex software with Excel, by simply inserting the default formulas into a spreadsheet, but sometimes it is feasible to modify default formulas to create complex software devices.  For example, I modified Microsoft Excelís functions that are used for time and date, (NOW() and TODAY(), to create a semi-random number generator, which transmits its numbers to ten calculation devices.  This software was also designed to illustrate some of the concepts used to create software with Microsoft Excel, and it is embedded in the lower section of this webpage.  The details about this software, is provided at the following website:  

 www.TechForText.com/Multiple-Calculation-Software-with-A-Semi-Random-Number-Generator-Based-On-Time 

 

            Another reason why Microsoft Excel can be used as a programming language is it can be electronically translated into a few conventional computer languages, with *specialized software.  I usually, create JavaScript software, in this way, which is comprised of both JavaScript and HTML code.  The JavaScript is used for the calculation mechanisms, and HTML is used for text and links.  The resulting code, can be edited, and/or cut and pasted into a conventional HTML webpage, using Notepad, or an HTML editor.

            *NOTE For translating Microsoft Excel devices, into JavaScript and HTML, I use SpreadsheetConverter, which is manufactured by Framtidsforum I&M AB, Sweden.  There website is www.SpreadsheetConverter.com.

            The following nine websites, contain free software downloads, that were created with Microsoft Excel, which demonstrate how Excel can be used as a programming language.

 

 

Website-1) A Calculation Device That Functions as a Calculus Tutorial

For Integrals with the Hyperbolic Sine snd Cosine

 

TITLE OF WEBSITE:

A Software-Based Tutorial On Calculus,

With The Hyperbolic Functions Sinh And Cosh

 

www.TechForText.com/Sinh-Cosh

 

If you want a printer friendly JavaScript version

of the software left click on this link

 

Left click here to download (Excel versions) in a zipped folder

Remove the software from the folder before you use it

 

1)DESCRIPTION: The calculation device on Website-1 is designed to function as a tutorial, for students to practice solving integrals, with the hyperbolic sine and cosine(sinh and cosh)  The calculation device-tutorial functions as soon as the user enters two numbers, in two white input boxes, on the top of the calculation device.  When this is done, the software generates, ten integral problems involving hyperbolic functions, with the numbers the user entered.  The calculated results for each problem are only revealed after the student attempts to solve the problem, by entering the numbers he or she calculated, into the input box of the problem in question.  If the student entered the correct answer, a message in green type is displayed.  If the student entered an incorrect answer, the software displays an error message in red type.             

            This software also has a device that keeps track of the number of correct calculations the student entered in the tutorial.  There are 10 problems generated by the software, and for each correct calculation entered by the student, the counting device displays 10%

            This software has another interesting feature, which allows the user to control the number of decimal places used in the calculations.  Specifically, on the upper section of the software, there is a white input box, and related text that indicate how many decimal places are going to be used for the calculations.  The users can change these settings, by deleting the number in the input box, and entering a number that represents the number of decimal places they prefer.

            On the very bottom of the software, there is a box to enter comments, and a submit button.  When the submit button is pressed, the entire calculation device, along with the calculated results, and the comments, are transmitted to my e-mail (David Alderoty).  In addition, each of the ten problems, has its own box to enter comments, but the submit buttons are located only on the bottom of the software.
            For students that need additional mathematics instruction, I provided links under each problem to access the
Wolfram Alpha computer.  This is a useful Internet resource, which can provide step-by-step solutions to mathematics problems.

http://www.techfortext.com/Tanh-Coth/Tanh-Coth.htm

 

Website-2) A Calculation Device That Functions as a Calculus Tutorial

For Integrals with the Hyperbolic Tangent And Cotangent

 

TITLE OF WEBSITE:

A Software-Based Tutorial on Calculus,

With The Hyperbolic Tangent and Cotangent

 

www.TechForText.com/Tanh-Coth

 

If you want a printer friendly JavaScript

version of the software left click on this link

 

Left click here to download the zipped folder

Remove the software from the folder before you use it

 

2)DESCRIPTION: The software on website-2 is similar to the above, except it is a calculation device and tutorial for integrals involving the hyperbolic TANGENT and COTANGENT.  

 

 

 

Website-3) A Calculation Device That Functions as a Calculus Tutorial

For Integrals with the Hyperbolic Secant and Cosecant

 

TITLE OF WEBSITE:

An Online Computer Tutorial on Calculus,

For The Hyperbolic Functions Sech and Csch

 

www.TechForText.com/Sech-Csch

 

If you want a printer friendly version of the

JavaScript tutorial, without the introductory

and instructional text, left click on these words.

 

Left click here to download a zipped folder with Excel versions.

Remove the software from the folder before you use it

 

3)DESCRIPTION: The software on website-3 is similar to the above, except it is a calculation device and tutorial for integrals involving the hyperbolic SECANT and COSECANT.

 

 

 

Website-4) A Calculation Device for Hyperbolic-Functions

 

TITLE OF WEBSITE:

An Online Calculation Device For Hyperbolic Functions,

And Related Mathematical Concepts

 

www.TechForText.com/Hyperbolic-Functions

 

For a printer friendly JavaScript version of the above without

introductory and instructional text, left click on these words.

 

Left click here to download the zipped folder, with Excel versions.

Remove the software from the folder before you use it

 

4)DESCRIPTION: The software on website-4, is a calculation device for calculating the HYPERBOLIC: sine, cosine, tangent, cotangent, secant, and cosecant.  The calculations take place, as soon as the user enters a number in a white input box, and clicks with the mouse.  Each of the six calculations are performed in two ways, one is with the Microsoft Excelís built-in functions, and the other is with the conventional formulas used for the hyperbolic functions, which are based on e (e = 2.718281828459050).  

            On the very bottom of this calculation device, there is a box to enter comments, and a submit button.  When the submit button is pressed, the entire calculation device, along with the calculated results, and the comments, are sent to my e-mail (David Alderoty). 

 

 

 

Website-5) A Calculation Device That Functions as a

Calculus Tutorial for Triple Integrals

 

TITLE OF WEBSITE:

Online JavaScript Calculation Software

For A Calculus Tutorial On Triple Integrals

 

www.TechForText.com/Triple-Integrals

 

For a printer friendly JavaScript version of the tutorial,

without introductory text, left click on these words.

 

Left click here to download a zipped folder, with Excel versions.

Remove the software from the folder before you use it

 

5)DESCRIPTION: The software on website-5 consists of a calculation device that functions as a tutorial for triple integrals.  When the user enters two numbers, in white input boxes on top of the calculation device, an additional four values are generated by the computer.  With these numbers, the software generates ten math problems in the form of triple integrals.  When the user enters numbers he or she calculated for a specific problem, the software checks the calculated results, and displays a message indicating whether or not the user entered the correct calculations.

            The calculations performed by this software are normally concealed, until the user enters manually calculated results.  However, if the user places an X in a green input box, on the top of the device, all the results calculated by the computer are displayed instantaneously.

            This software also has a device that keeps track of the number of correct calculations the student entered in the tutorial.  There are 10 problems in the software, and for each correct calculation, the counting device displays 10% 

            This software has another interesting feature, which allows the user to control the number of decimal places used in the calculations.  Specifically, on the upper section of the software, there is a white input box, and related text that indicate how many decimal places are going to be used for the calculations.  The users can change these settings, by deleting the number in the input box, and replacing it with a number that represents their preferred number of decimal places.

            On the very bottom of this calculation device, there is a box to enter comments, and a submit button.  When the submit button is pressed, the entire calculation device, along with the calculated results, and the comments, are sent to my e-mail (David Alderoty). 

 

 

Website-6) A Calculation Device That Functions as a Tutorial for

Solving Algebraic Equations with Hyperbolic Functions

 

TITLE OF WEBSITE:

Online Tutorial on Algebra with Hyperbolic Functions

In The Form of JavaScript Calculation Software

 

www.TechForText.com/Algebra-with-Hyperbolic-Functions

If you want a printer friendly JavaScript version of this software,

without the introductory text left click on these words

 

Left click here to download a zipped folder, with Excel versions.

Remove the software from the folder before you use it

 

6)DESCRIPTION: The software on website-6 consists of a calculation device that functions as a tutorial for algebra problems with hyperbolic functions.  When the user enters two numbers in the input boxes, a set of semi-random numbers are generated.  The software uses these numbers to generate ten algebra problems involving hyperbolic functions.  When this is done, the software instantly calculates the answers to the ten algebra problems, and generates step-by-step solutions for each of the problems.  The calculated results and a step-by-step solution are initially concealed from the user.  When the user enters a manually calculated result, into an input box for a specific problem, the software displays the correct calculated result, and the step-by-step solution to the problem.  If the user entered the correct calculated result, a message in green type is displayed.  When an incorrect result is entered by the user a message in red type is displayed.

            The calculations performed by this software are normally concealed, until the user enters manually calculated results.  However, if the user places an X in a green input box, on top of the calculation device, all the results calculated by the computer are displayed instantaneously.

            This software also has a device that keeps track of the number of correct calculations the student entered in the tutorial.  There are 10 problems in the software, and for each correct calculation, the counting device displays 10% 

            This software has another interesting feature, which allows the user to control the number of decimal places used in the calculations.  Specifically, on the upper section of the software, there is a white input box, and related text that indicate how many decimal places are going to be used for the calculations.  Users can change these settings, by changing the number in the input box.

            On the very bottom of this calculation device, there is a box to enter comments, and a submit button.  When the submit button is pressed, the entire calculation device, along with the calculated results, and the comments, are transmitted to my e-mail (David Alderoty).  In addition, each of the ten problems, has its own box to enter comments, but the submit buttons are located only on the bottom of the software.

 

 

 

Website-7) A Calculation Device That Calculates

The Average, and a Few Other Statistical Calculations

 

TITLE OF WEBSITE:

Online Table for Calculating the Average

 

www.TechForText.com/Online-Table-for-Calculating-the-Average

 

If you want a printer friendly JavaScript version of this software,

without the introductory text left click on these words

 

7)DESCRIPTION:  The software on website-7 consists of a JavaScript online calculation device, which calculates the average when a set of numbers (or scores) are entered in column C.  It also calculates three other components that relate to each individual score, which are displayed in three columns D, E, and F.  This software can handle up to 40 numbers (or scores), and it has a print button, so users can print their calculated results.

 

 

 

Website-8) Databases with Calculation Devices

 

TITLE OF WEBSITE:

Calculating-Spreadsheet-Databases

Created with Microsoft Excel

 

www.TechForText.com/Calculating-Spreadsheet-Databases

8)DESCRIPTION: Website-8 has a total of 20 downloadable databases, and the website contains over 5500 words, and it has its own hyperlinked table of contents.  The databases do not contain any data.  They are designed for individuals, businesses, and organizations who want to store their own information in their own database.  The databases require Microsoft Excel 2003, 2007 or 2010, or later versions, and they can be obtained for free, by downloading from the website listed above.

            All of the databases on website-8 have some type of calculation mechanism, such as to count the number of entries, or to perform statistical calculations.  These databases also have the Microsoft Excel alphabetizing device installed, on the very top of each column.  With this device you can alphabetize anything in the column, from A to Z, or from Z to A.  The alphabetizing device also has a search mechanism.  

            Six of these databases I design specifically for multiple lines of text.  Nine of the databases have calculation mechanisms that perform various types of statistical calculations.  In addition, I created five databases that are designed to hold hyperlinks to various types of digital media, such as websites, videos, Microsoft Word documents, Excel spreadsheets, PDF files, etc.  

 

 

 

Website-9) A Multiple Calculation Device with

A Semi-Random Number Generator

 

TITLE OF WEBSITE:

Multiple Calculation Software, with a

Semi-Random Number Generator, Based on Time

 

www.TechForText.com/Multiple-Calculation-Software-with-A-Semi-Random-Number-Generator-Based-On-Time

 

If you want a printer friendly, JavaScript version of this software,

without the text on the website, left click on these words.

 

Download link for a zipped folder,

with Excel versions of the software.

Remove the files from the folder, before you use them.

 

9)DESCRIPTION: The software on website-9, was briefly mentioned, on the upper section of this webpage. This is a very unusual device, and it is about 30 pages in length, without the website.  With the website it is 37 pages.  It has a semi-random number generator that uses the computerís clock and a series of formulas I created, to generate sets of random numbers.  The random numbers are transmitted within the software, to ten calculation devices, that carry out OVER 60 calculation simultaneously, involving algebra, trigonometry, calculus, and geometric calculations for a circle and rectangle.

            This software demonstrates how Microsoft Excel can be used as a computer language, to create complex software.  The spreadsheet formulas and the related connections are displayed in the first section of the software, using black lines to show the data transfer from input boxes, and from one formula to another.  The second and third sections of the software display only the spreadsheet formulas. 

            The Multiple Calculation Software, with a Semi-Random Number Generator is embedded in website‑9, shown above, but I am also embedding it in this webpage, because it illustrates some of the most important concept for creating software with Microsoft Excel.  If you want a printer friendly, JavaScript version, of this software, without the text on this webpage, left click on these words.

 
    Multiple Calculation Software, with a Semi-Random Number Generator Based on Time          
Created by David Alderoty © 2012, E-mail David@TechForText.com
  This calculation software was created to demonstrate some of the ways that Microsoft Excel can be used as a programming language. For this calculation device, I created a semi-random number generator, using Microsoft Excel's NOW() and TODAY() functions, so that the computerís clock is used to generate sets of random numbers. These numbers are transmitted to 10 calculation mechanisms, which perform various types of calculations, including algebra, trigonometry, and calculus.  
   
 

This software was initially created with Microsoft Excel, which actually can be converted electronically to a few standard computer languages, using specialized software. I converted this software device to a JavaScript/HTML format, which functions over the Internet, in standard web browsers.                         

                                                     

 
Section 1) The Semi-Random Number Generator
  This section displays the semi-random number generator, and a useful conceptualization for creating software with Microsoft Excel. Specifically, the formulas comprising software can be connected together in various configurations, with virtual wires. This is similar to the way electronic circuits are created. This basically involves input boxes and formulas transmitting numbers or calculated results to other formulas for additional calculations. This can involve configurations involving hundreds of connections, and many virtual wires. The virtual wires are of course mental conceptualizations that are normally invisible in the software, but in this section I created black line showing the connections for one formula to another. Most of the virtual wires are displayed on the right.  
   
   
  Note: The computations are displayed in red numbers and text. The spreadsheet formulas are displayed in black type, with an equal-sign on the left side, such as the following example:  
  =IF(C36>8,H27,H25)  
  By default the software, automatically changes most of the random numbers, when you enter or delete data, or press the update button. This is actually based on time intervals ranging from a second or less.  
  If you want to control the length of time before the random numbers are changed, enter the time duration you prefer in minutes in the white box below. If you want to maintain the random numbers until 12 AM, enter 1440 in the box below. If you want to maintain them for one hour, enter 60, for two hours 120, etc. If you want the random numbers to change, in a matter of seconds, enter 0.01667 for each second. For 30 seconds enter 0.5, for 15 seconds enter 0.25. However, regardless of the numbers you enter, at 12 AM the random numbers are automatically changed.  
   
   
]   Input Box One>   virtual wire    
                             
    IMPORTANT NOTE: The numbers do not change, if you do NOT update the time. To update the timing mechanism for the Excel version, place the cruiser on a green box, and press the delete key. For the JavaScript version, press the update button, with the words: LEFT CLICK TO UPDATE TIME. You can also update the time by entering or deleting data, or closing and reopening the software,which works for both the Excel and JavaScript versions.        
       
       
      virtual wire>    
             
             
             
  The four black boxes on the right are storage devices for the messages, which are displayed in red type above and below. These messages change when the user enters numbers in the white input box BELOW. The formulas used to sense whether or not numbers were entered in the white box, and to switch the messages that are displayed, are:                    
      The software is set to generate random numbers using the computerís clock, which it will automatically transmit to the 10 calculation mechanisms.            
  For the message above =IF(C37>8,H28,H26) For the message below) =IF(C37>8,H33,H31)                    
              The software will generate random numbers, WITH THE NUMBER YOU ENTERED IN THE WHITE BOX, and then it will transmit these numbers to the 11 calculation mechanisms.            
                         
                     
      If you do NOT want to use the computerís clock to generate random numbers, enter a number in the white box below, with nine or more digits.            
                     
      IF YOU WANT TO USE THE COMPUTERíS CLOCK TO GENERATE RANDOM NUMBERS, delete the number in the white box below. When this is done, the software will use the computers timing mechanism to generate sets of random numbers.            
    Input Box Two                    
                       
          virtual wire        
                       
  The above counts the number of digits entered by the user, with this formula: =(LEN(C39)*1)-1*(C35=0), and then transmits the results to other formulas for additional computation.        
    virtual wire            
  The above takes the absolute value of the number entered by the user, with this formula: =ABS(C35), and transmits it to other formulas for additional processing.                
  virtual wire              
  The above is box-1W, and it uses Microsoft Excel =NOW() function to access the computerís clock. With the following formatting code the time and a is displayed with this function: dddd, mmmm d, yyyy, h:mm:ss AM/PM              
                         
  Note, there are two number generating systems, that use the computerís clock to generate semi-random numbers. One system, is represented by white boxes, and the other system by light blue boxes. The first system, with the white boxes, does NOT provide user control of time intervals, for generating numbers. However, the second system, with the blue boxes, uses the number of minutes entered by the user, to control time intervals, for generating new sets of numbers.              
                     
  The above is box-2W, and it uses Microsoft Excel's =TODAY() function to access the computerís clock, which displays today's date, in the style presented above. This requires the following custom formatting code: "Today is" dddd, mmmm d, yyyy                  
                       
                       
  <virtual wire The above is box-3W, and it, accesses the cell with the =NOW()and TODAY() function, and subtracts as follows: TODAY()-NOW(). This is done with the following formula: =B41-B45            
             
  <virtual wire The above, is an automatic switching device, which senses if the user entered a number with nine digits or more in the white input box above, which is done with =IF(C37>8, C39, C47) If the user entered the number, with the required number of digits, the connections to the white input box are activated, and the connections that relate to the computers clock are turned off. If the user did not enter a number, the connections to the computerís clock are maintained. All of this results in one number, which is user entered, or computer-generated, which is transmitted to other formulas for further processing.      
  virtual wire>      
  <virtual wire Box1B, above, and box-2B, and box-3B, below, comprise a separate number generating system that uses the computerís clock to generate semi-random numbers, based on a time interval set by the user. Box-1B generates a three digit number, with the following formula: =RIGHT(TODAY(),3)                    
                       
                       
  <virtual wire     virtual wire >              
        < virtual wires >      
    Box-2B, above, generates a single digit number, with the following formula:                    
  =1*(RIGHT((TRUNC(((NOW()*24*60))/(D16)))))                    
             
  Box-4W, above, generates a number, with nine or more digits, without decimals, based on input from the computer's clock, or from a number entered by the user, in input box two. This is done with the following formula: < virtual wires > Box-3B, above generates, a number over nine digits long, with the data input for box-1B and Box-2B. This is done with the following formula: =1*(C52*(((2*TT+3&((TT=0)+TT)&(2*TT+1)&2*TT+3))^2))      
=ROUND(1000000000*$C$50,0) < virtual wires >      
    virtual wires    
  The box above, is an automatic sensing and switching mechanism. That is, based on numbers that the user entered or did NOT enter in the three white input boxes above, the switching mechanism selects one of the following for random number generation: 1)Default settings, 2)User selected time intervals, 3)User entered number, without using the computerís clock. The formula I devised to carry out this task is: =IF(C37>8, C39, IF(D16=0, C60, E60))                    
                     
                     
                       
    The above, accesses the first digit of the number generated by the computer's clock, or with the number entered by the user. This number has nine or more digits. The formula I devised to access the first digit is as follows: =1*RIGHT(LEFT($C$63,1)) The cell with this formula was renamed as: Digit1, so that Digit1 will equal the first digit. See below.                
                   
                       
    The above, accesses the second digit, with the following formula: =1*RIGHT(LEFT($C$63,2)) The cell with this formula was renamed Digit2 so that =Digit2, will display the second digit. See below.              
                   
                       
    The above, accesses the third digit, with the following formula: =1*RIGHT(LEFT($C$63,3)) The cell with this formula was renamed Digit3 so that =Digit3, will display the third digit. See below.              
    virtual wire            
                       
    The above, accesses the fourth digit, with the following formula: =1*RIGHT(LEFT($C$63,4)) The cell with this formula was renamed Digit4 so that =Digit4, will display the fourth digit. See below.            
             
                         
      virtual wire          
                       
    The above, accesses the fifth digit, with the following formula: =1*RIGHT(LEFT($C$63,5)) The cell with this formula was renamed Digit5 so that =Digit5, will display the fourth digit. See below.            
    virtual wire        
                       
    The above, accesses the sixth digit, with the following formula: =1*RIGHT(LEFT($C$63,6)) The cell with this formula was renamed Digit5 so that =Digit5, will display the sixth digit. See below.            
    virtual wire      
                       
    The above, accesses the seventh digit, with the following formula: =1*RIGHT(LEFT($C$63,7)) The cell with this formula was renamed Digit7 so that =Digit7, will display the seventh digit. See below.            
                       
                         
        virtual wire    
                       
    The above, accesses the eighth digit, with the following formula: =1*RIGHT(LEFT($C$63,8)) The cell with this formula was renamed Digit8 so that =Digit8, will display the eighth digit. See below.            
      virtual wire  
                       
    The above, accesses the ninth digit, with the following formula: =1*RIGHT(LEFT($C$63,9)) The cell with this formula was renamed Digit9 so that =Digit9, will display the ninth digit. See below.            
                       
  Generating A Second And Third Set Of  
Semi-Random Numbers From the First Set
  In this section, the software generates a second and third set of semi-random numbers from the first set. There are actually a large number of ways that this could be achieved. This software uses mathematical formulas to generate the second set, and the rearrangement of digits to generate the third set. This should be clear after you examine the material in this section.  
   
  In the previous section, I demonstrated the connections between formulas, by displaying virtual wires, in black type connecting the formulas together, in various configurations. In this section, the connections between formulas, and cells are implied, when the name of a cell is used in a formula. For example, if I create a formula with =A1+B1, and place it in cell D5, it should be apparent that the formula in cell D5 is accessing the numbers, or calculated results in cells A1 and B1, and adding them together. This can be thought of as virtual wires transmitting data from cells A1 and B1 to cell D5, to perform the addition.  
   
   
  Some of the cells have been renamed, so that is easier to remember what the formulas in the cells generate. For example, cell Digit1, displays the first digit from the semi-random number generated in the previous section. Similarly, cell Digit2, displays the second, Digit3 displays the third, etc. The following formulas uses the cell designations Digit1 to Digit9, to generate a third set of numbers, which range from 0.1 to 1. These limits are the result of the design of the formula used to generate the second set. See below:  
   
   
  The formula used for the following is: =(DigitX+1)/10  
The value of X in this formula rangers from 1 to 9
       
  Digit1 = = cell named DigitS1  
  Digit2 = = cell named DigitS2  
  Digit3 = = cell named DigitS3  
  Digit4 = = cell named DigitS4  
  Digit5 = = cell named DigitS5  
  Digit6 = = cell named DigitS6  
  Digit7 = = cell named DigitS7  
  Digit8 = = cell named DigitS8  
  Digit9 = = cell named DigitS9  
  The sum of the digits The sum of the small digits  
   
  Above cell renamed SUM The above cell renamed sumS  
  Formula for above is The formula for the above is  
  =SUM(C111:C119) =SUM(D111:D119)  
  Average of the digits Average of the small digits is:  
   
  The above cell was Above cell renamed as digitSA  
  renamed as DigitA The formula for the above is  
  Formula for above is: =sumS/9  
  =SUM/9                        
         
  The Following List of Semi-Random Numbers, were Created Above, in This Section.            
   
   
   
   
   
   
   
   
   
   
   
   
   
                             
         
  The above random numbers were created with formulas, using conventional mathematics. The list of random numbers presented below were created by recombining digits in various configurations. (The digits I am referring to were created in section 1, and they are Digit1, Digit2, Digit3, Digit4, Digit5, Digit6, Digit7, Digit8, and Digit9.)  
   
  This rearranging of the digits does not involve conventional mathematics. The general formula I devise for this process consists of the following: =1*((DigitX=0)+DigitX&DigitY). X and Y in this formula represent any number from 1to9.  
   
  The first part of this formula is designed to prevent a number with a zero as the first digit. That is if the random number for DigitX turns out to be zero, the statement (DigitX=0) would be true. True statement are represented by 1 in Microsoft Excel, especially if they are multiplied by 1. The 1 is added to the zero, which provides 1 as the first digit. If DigitX does not equal zero, this statement DigitX=0 is false. False statements in Microsoft Excel are represented by zero, which does not change the value of the first digit.  
   
  The second portion of the formula, involves a method of combining digits, or mathematical expressions, using the & sign. For example, =1*(2&5)=25. Alternatively this can be achieved with 0+(2&5)=25. It is necessary to multiplied by 1, or to add 0 to the number, so that it is converted to a true number that can be used in mathematical calculations. The above might sound strange, but it works quite well,which will be apparent if you examine the following material.  
   
   
         
                 
    (The cell below was renamed as: A) A Semi-random two digit number is generated with the formula presented below:            
    =1*(((Digit6=0)+Digit6)&Digit9)            
               
                             
    (The cell below was renamed as: B) A Semi-random two digit number is generated with the formula presented below:            
    =1*(((Digit9=0)+Digit9)&Digit5)            
               
                             
    (The cell below was renamed as:C_) A Semi-random two digit number is generated with the formula presented below:            
    =1*(((Digit8=0)+Digit8)&Digit7)            
               
                             
    (The cell below was renamed as: D) A Semi-random two digit number is generated with the formula presented below:            
    =1*(((Digit5=0)+Digit5)&Digit6)            
               
                             
    (The cell below was renamed as: E) A Semi-random two digit number is generated with the formula presented below:            
    =1*(((Digit7=0)+Digit7)&Digit9&Digit4)            
               
                             
    (The cell below was renamed as: F) A Semi-random three digit number is generated with the formula presented below:            
    =(1*(Digit5=0)+Digit5)&Digit7&Digit8            
               
                             
    (The cell below was renamed as: G) A Semi-random three digit number is generated with the formula presented below:            
    =1*(((Digit6=0)+Digit6)&Digit5&Digit9)            
               
             
    (The above cell was renamed as: H) A Semi-random three digit number is generated with the formula presented below:            
    =1*(((Digit8=0)+Digit8)&Digit7&Digit6)            
               
                           
     
The Following Semi-Random Numbers were Created Above, in This Section            
   
   
   
   
   
   
   
   
                             
Section 3) 10 Calculation Devices, that Use the Semi-Random Numbers, for Algebra, Trigonometry, Calculus, and
  the Geometric Calculations for a Circle and Square  
  In this section, there are 10 calculation devices, that receive some of the random numbers generated in the first two sections of this software. These devices perform various types of calculations, involving algebra, trigonometry, calculus, and geometric calculations for a circle and square. Each of these devices, performs a series of multiple calculations simultaneously.  
Calculation Mechanism 1) Algebraic Equation
with a Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  =A&"X+"&B&" = "&C_  
   
  ="X"&A&"= "&C_&-B  
   
  =A&"X= "&C_-B  
    X=  
  =(C_-B)/A  
  The calculations are check below  
   
  =A*D215&"+("&B&") = "&C_  
   
  =A*D215+B&"="&C_  
         
Calculation Mechanism 2) Algebraic Equation
with Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  =D&"X+"&E&" = "&F  
   
  ="X"&D&"= "&F&-E  
   
  =D&"1X= "&F-E  
    X =  
  =(F-E)/D  
  The calculations are check below  
   
  =D*D233&"+("&E&") = "&F  
   
  =D*D233+E&"="&F  
         
Calculation Mechanism 3) Algebraic Equation
with Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  =(1+Digit6)&"X+"&H&" = "&F*A  
   
  =(1+Digit6)&"X="&F*A&"-"&H  
   
  =(1+Digit6)&"X="&F*A-H  
    X =  
  =(F*A-H)/(1+Digit6)  
  The calculations are check below  
   
  =(1+Digit6)*D251&"+"&H&" = "&F*A  
   
  =(1+Digit6)*D251+H&" = "&F*A  
       
Calculation Mechanism 4) Algebraic Equation Involving
the Hyperbolic Tangent, with Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  ="TANH("&A&")X+"&"TANH("&B&") = "&C_  
   
  ="TANH("&A&")X= "&C_&"-"&"TANH("&B&")"  
   
  ="TANH("&A&")X="&C_&"-"&TANH(B)  
   
  =TANH(A)&"X="&C_&"-"&TANH(B)  
    X=  
  =(C_-TANH(B))/TANH(A)  
  The calculations are check below  
   
  ="TANH("&A&")"&D271&"+"&"TANH("&B&") = "&C_  
   
  =TANH(A)*D271&"+"&TANH(B)& "= "&C_  
   
  =TANH(A)*D271+TANH(B)&"= "&C_  
         
Calculation Mechanism 5) Algebraic Equation Involving
the Hyperbolic Tangent, with Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  ="TANH("&(Digit7+1)&")X+"&"TANH("&(Digit5+3)&") = "&A*(Digit7+1)  
   
  ="TANH("&(Digit7+1)&")X= "&A*(Digit7+1)&"-"&"TANH("&(Digit5+3)&")"  
   
  ="TANH("&(Digit7+1)&")X="&A*(Digit7+1)&"-"&TANH((Digit5+3))  
   
  =TANH((Digit7+1))&"X="&A*(Digit7+1)&"-"&TANH((Digit5+3))  
    X=  
  =(A*(Digit7+1)-TANH((Digit5+3)))/TANH((Digit7+1))  
  The calculations are check below  
   
  ="TANH("&(Digit7+1)&")"&D293&"+"&"TANH("&(Digit5+3)&") = "&A*(Digit7+1)  
   
  =TANH((Digit7+1))*D293&"+"&TANH((Digit5+3))& "= "&A*(Digit7+1)  
   
  =TANH((Digit7+1))*D293+TANH((Digit5+3))&"= "&A*(Digit7+1)  
       
Calculation Mechanism 6) Algebraic Equation Involving
the Hyperbolic sine and cosine, with Step-By-Step Solution
  Spreadsheet formulas are displayed in black type, within =  
  The calculated result are displayed in red type.  
   
  ="SINH("&(DigitS7)&")X+"&"COSH("&(DigitS5)&") = "&A*(DigitS7)  
   
  ="SINH("&(DigitS7)&")X= "&A*(DigitS7)&"-"&"COSH("&(DigitS5)&")"  
   
  ="SINH("&(DigitS7)&")X="&A*(DigitS7)&"-"&COSH((DigitS5))  
   
  =SINH((DigitS7))&"X="&A*(DigitS7)&"-"&COSH((DigitS5+3))  
    X=  
  =(A*(DigitS7)-COSH((DigitS5)))/SINH((DigitS7))  
  The calculations are check below  
   
  ="SINH("&(DigitS7)&")"&D315&"+"&"COSH("&(DigitS5)&") = "&A*(DigitS7)  
   
  =SINH((DigitS7))*D315&"+"&COSH((DigitS5))& "= "&A*(DigitS7)  
   
  =SINH((DigitS7))*D315+COSH((DigitS5))&"= "&A*(DigitS7)  
       
  Calculation Mechanism 7) Performs over 15  
  Trigonometric Calculations, Simultaneously.  
   
   
Angles rounded to decimal places
Numbers rounded to decimal places
  The spreadsheet formulas are displayed in black type, with =  
  Calculated result are displayed in red type  
       
  ="Angle B= "&ROUND(ATAN(tanB),RD)&" Radians"  
     
="Angle B= "& ROUND(DEGREES(ATAN(tanB)),RD )&" Degrees"
                             
      Hypotenuse Cell renamed: hyp is:
     
    =ROUND((A*A+B*B)^(1/2),RN )
                             
       
   
    ="Angle A = "&ROUND(ATAN(tanA),RD)&" Radians"
     
="Angle A= "& ROUND(DEGREES(ATAN(tanA)),RD )&" Degrees"
="The perimeter of the triangle is "&ROUND(A+B+(A*A+B*B)^(1/2),RN)
="The area of the triangle is "&ROUND((A*B)/2,RN)
       
                             
 
 
                           
="&ROUND(A/hyp,RN)
 
 
 
 
                           
="="&ROUND(B/hyp, RN)
 
                             
 
 
                           
="="& ROUND(A/B,RN)
   
                             
 
 
                           
="="&ROUND(B/A,RN)
   
         
   
  ="Tan(A)*Cot(A)="&tanA*cotA  
                             
 
 
                           
  ="="&ROUND(hyp/B,RN)  
   
                             
   
  ="cos(A)*sec(Angle A)="&cosA*secA  
 
 
 
  ="&ROUND(hyp/A,RN)  
                           
   
                             
   
  ="sin(A)*csc(A) = "&sinA*cscA  
         
  The Following Trigonometric Calculations Are For Angle B  
   
   
                             
 
 
  ="="&ROUND(B/hyp,RN)  
                           
 
 
 
 
  "= "&ROUND(A/hyp, RN)  
                           
 
 
 
 
  ="="& ROUND(B/A,RN)  
                           
   
                             
 
 
  ="="&ROUND(A/B,RN)  
                           
   
                             
   
  ="Tan(A)*Cot(A)="&tanA*cotA  
                             
 
 
  ="="&ROUND(hyp/A,RN)  
                           
   
                             
   
  ="cos(B)*sec(B) = "&ROUND(cosB*secB,5)  
 
 
 
  ="="&ROUND(hyp/B, RN)  
                           
   
       
  The Following Trigonometric Calculations Apply To Both Angles A and B  
                             
   
  ="sin(B)*csc(B)="&sinB*cscB  
      2 2                    
    sin(A) +  cos(A)  
  ="="&ROUND(sinA*sinA+cosA*cosA,RN)  
      2 2                    
    sin(A) +  sin(B)  
  ="="&ROUND(sinA*sinA+sinB*sinB, RN)  
      2 2                    
    cos(A) +   cos(B)  
  ="="&ROUND(cosA*cosA+cosB*cosB,RN)  
     
      -2 -2                    
    csc(A) +   sec(A)  
  =" = "&ROUND((cscA^(-2))+(secA^(-2)),RN)  
      2.5 2.5                    
    sin(A) +  cos(A)  
  ="="&ROUND((sinA^2.5)+(cosA^2.5), RN)  
      3 3                    
    sin(A) +  cos(A)  
  ="="&ROUND((sinA^3)+(cosA^3),RN)  
      4 4                    
    sin(A) +  cos(A)  
  ="="&ROUND((sinA^4)+(cosA^4),RN)  
                             
   
  ="sin(A)+cos(A) = "&ROUND(sinA+cosA,RN)  
                             
   
  ="tan(A)+cot(A) = "&ROUND(tanA+cotA,RN)  
                             
   
  ="csc(A)+sec(A) = "&ROUND(cscA+secA,RN)  
       
Calculation Mechanism 8) Calculations For A Rectangle
    The spreadsheet formulas are displayed in black type within = and the calculated result are displayed in red type.          
                             
                         
                         
 
    ="The perimeter is "&2*G+2*H
                         
   
  ="The area is "&G*H
 
       
Calculation Mechanism 9) Calculations For A Circle
    The spreadsheet formulas are displayed in black type within = and the calculated result are displayed in red type.          
                             
       
      ="The radius is "&C_  
                             
       
      ="The diameter is "&2*C_  
                             
   
  ="The perimeter is "&2*PI()*C_  
   
  ="The area is "&PI()*(C_*C_)  
       
Calculation Mechanism 10) Calculus
  The spreadsheet formulas are displayed in black type within = and the calculated result are displayed in red type.  
     
                           
                             
                           
                 
  ="dx = "&A-B    
                           
                           
                 
                             
                           
                             
                           
                 
  =" xdx = "&(G*G-H*H)/2  
                           
                           
                 
                             
                           
                             
                           
                 
  =G&"xdx = "&G*((D*D-C_*C_)/2)  
                           
                           
                             
                             
                           
                             
                           
                 
  =G*B&"xdx = "&G*B*((digitSA*digitSA-DigitS1*DigitS1)/2)