# Graphing Calculator’s History and Usage

## History of calculator

The electronic calculator is a vivid example of how accelerating the speed of technological change may be. The abacus, which is also called a counting frame, is known to have been used by Babylonians in 3000 BC to calculate arithmetical processes (“Chronological calculator timeline,” n.d., para. 3). The abacus had ten beads on each rod, which showed the number of tens and hundreds. Addition and subtraction were performed by moving one bead across the next. This early form of calculator spread rapidly throughout Asian countries, Egypt, and Greece, and was used for the next three centuries. In 1300 BC, the Chinese redesigned the abacus, so it had two beads above the crossbar and five beads below. Curiously enough, abaci are still being used by some merchants in Japan and China.

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It was only at the beginning of the seventeenth century that the first mechanical calculators began to appear in Europe. The slide rule, or a slipstick, was invented by William Gunter after his developing a logarithmic rule for multiplication and division. Slide rules evolved to allow such functions as exponents, roots, and trigonometry. In 1623, the “calculating clock” that was based on gears was invented by the German scientist Wilhelm Schickard (Williams, 2017). The machine was designed to help with four basic arithmetical operations, such as addition, subtraction, multiplication, and division. This mechanical calculator could add and subtract numbers with no more than six digits and even had a memory register.

Twenty years later, Pascal was led to develop a mechanical calculator or Pascaline by complex and time-consuming arithmetical operations, which his father did while working as a supervisor of taxes. Pascal received a Royal Privilege giving him exclusive rights to sell Pascalines in France, yet the complexity and cost of the machine were the main barriers to sales (Harris, 2019). Gottfried Leibniz developed the stepped reckoner (or stepped reckoner), a digital mechanical calculator in 1673, which, though, failed to become a fully operational machine.

The first calculator that was strong and reliable enough to be used in the daily working environment appeared only at the beginning of the nineteenth century when Charles Xavier Thomas designed an arithmometer. The machine could add and subtract two numbers directly and perform complex division and multiplication using a movable accumulator (Harris, 2019). The arithmometer played a pivotal role in the move from human computers to commercially successful calculators.

It was not until 1902 that the first ten-key calculator was invented by James Dalton. The whole twentieth century saw the steady development of mechanical calculators with size reduction and user-friendly features. MADAS 20AZS was a mechanical electronically driven calculator with automatic multiplication and division. The first electronic desktop calculators that used cold-cathode vacuum tubes were developed in the middle of the twentieth century. It was Bell Punch Co. that announced their production for the European market. By the end of the twentieth century, these calculators ceased the production of their mechanical competitors.

The new transistor design of electronic calculators opened the floodgates to a new generation of calculating machines. First commercial transistorized calculators, Friden EC130 and Friden EC132 were sold at a price comparable to that of family cars (National Museum of American History, n.d.). The development of hand-held electronic calculators was started by Texas Instruments in 1965. At that time, a hand-held calculator was made of a few chips that were powered by rechargeable batteries. The Sharp Compet QT-8B is the first battery-powered hand-held calculator designed by Texas Instruments. Even though these calculators were costly, in quite a few years, they became available to almost everyone. The first American pocket-size calculator was the Bowmar 901B, or the Bowmar Brain, with an 8-digit red LED display.

Graphing calculators process several complex inputs at a time to plot a graph, solve simultaneous equations and do other tasks with quantitative variables. The first commercially viable graphing calculators were invented in 1985 and 1986 by Casio and Hewlett-Packard, respectively (National Museum of American History, n.d.). A couple of years later, Texas Instruments made a major lead, introducing its TI-81, which became preferred by educators due to the ability to work with several functions simultaneously and user-friendly design. In the two decades that followed, graphing calculators enjoyed several innovations, which improved their processing power and increased the display, thus showing mathematical expressions in a much more readable way.

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Graphing calculators are useful tools for students and teachers who need to generate graphs fast and easily. There are two manufacturers who dominate the market of these machines, Texas Instruments, and Casio. Texas Instruments is considered to be a golden standard for these calculators that are universal in secondary and post-secondary education. The TI-84 Plus CE graphing calculator by Texas Instruments is preloaded with a number of functions, such as data collection, graphing, and color-coded equations. The Casio fx-9750GII features a black-and-white LED display and the basic functionality of an entry-level graphing calculator. Among other companies that manufacture graphing calculators are HP, Sharp, Radio Shack, and Canon.

## Instruction Manual

Note: the given instruction manual is for the TI-84 Plus or TI-84 Plus Silver Edition graphing calculators. The use of this instruction manual for other graphing calculators is not recommended.

## How to Turn On the Graphing Calculator

• Ensure that the calculator has five batteries, of which four are triple-A alkaline batteries, and one is a silver oxide button cell backup battery for memory backup.
• Press “ON,” which is the black button located in the lower-left corner. An information screen displays a message that the shortcut menus are displayed upon pressing “ALPHA” + “F1”-“F4”.
• Press “1” to continue and skip this information screen the next time.
• Press “2” if you want to continue and see the information screen the next time.

## How to Turn Off the Graphing Calculator

Press the “2ND” blue button located in the top left corner and then the “ON” button in the lower-left corner.

## How to Graph a Circle

• Choose the FUNC mode by pressing the button labeled “MODE” that is located next to the “2ND” or “SHIFT” button.
• To display the Y-editor, press “Y=.” Identify the equation of the circle in the form of where m is the radius of the circle. Press “2ND”,” “(, “m” (your value), “-, “X,” “X2”, “).” Then press “ENTER” to enter the equation. “”
• Since the above-presented equation indicates only the upper half of the circle, one more function needs to be defined.
• Press “Y2=”, then press “-“ to enter the minus sign. Press “ALPHA” + “F4” to go to the menu of y-variable and select “Y1” by pressing “ENTER.”
• Instead of graphing the function, press “ZOOM” 6.
• To adjust the function which has appeared as an ellipse due to the range of values defined by standard, press “ZOOM” 5.
• Press “square” to see the values of Xmax, Xmin, Ymax, and Ymin variables.

## How to Enter Polar Equations

• Press “MODE” and put the calculator in the “POLAR MODE” by using the arrow keys to select the right mode and pressing “ENTER.” It should be mentioned that the polar mode must be selected before the equation or the values for the variable are entered.
• Select “RADIAN” or “DEGREE” mode, depending on how you want your polar equation to be graphed.
• For the other mode settings, select the options on the left.
• To access Format Menu, press “2ND” + “ZOOM.” Ensure that both “EXTRON” and “CORDON” are highlighted to trace your equations. Select “POLAR GC” and press “ENTER” to indicate that you want your coordinates to be displayed in a polar form.
• To display the polar Y= editor, press “Y=.” Enter your equation. In the Polar Y= editor, you can enter up to six equations, r1 through r6.
• Press “ALPHA” + “TRACE” to access the Y-VAR menu. Now you can save your time by entering all the other polar equations.
• You may change the color of the polar graph in the spinner menu. Press “ENTER” twice to apply the changes.
• Your polar equation may be edited in the Ensure that you have selected the function you want to edit with arrows. Edit the function by entering or editing the expression.
• Press “ZOOM” 5 to plot the graph.

## How to Enter and Store Matrices

• You can the perform addition or subtraction of matrices by using the MTRX shortcut menu on the home screen (“ALPHA” + “F3”). You can also go to them to create a matrix. If you want to divide two matrices, create an inverse matrix first. Then, multiply the inverse matrix by another matrix.
• After you have created a matrix, highlight “OK” using arrows and then press “ENTER.”
• Using arrows, enter the four values to create the first 2×2 matrix. You can use the minus sign to put a negative value.
• To create the second matrix, press “+” + “ALPHA” + “F3” + “ENTER” and enter the four values. Now you can perform the calculation with these two matrices.
• If you want to store the calculated matrix, press “STO” + “2ND” + “MATRIX,” select the matrix you want to store from the list, and press “ENTER.”
• The matrix will appear in the matrix editor, which you can access by entering “2ND” + “MTRX.”
• Go to the “EDIT” screen to select a matrix for editing.
• You can change matrix dimensions, which are highlighted by the cursor. To change the number of rows, enter a new number and press “ENTER.” Depending on available memory, a matrix may have no more than 99 rows and 99 columns.

## How to Create a Program that Computes the Volume of a Cylinder

• Press “PRGM” and go to “NEW” using arrows.
• Select “CREATE NEW” by pressing “ENTER.” Alpha-lock is on, so focus just on the green letters.
• Type the name of the program (PROGRAM) after NAME =. Press “ENTER.”
• Now you are the program editor. Press “PRGM” 2 to select “2:Prompt”. Press “ALPHA” to put the alpha lock off. Press “ALPHA” + “H” +, “+ “R.” R is the variable for radius, and H is the variable for height.
• Press “ENTER.”
• Press “2ND” + ” ” + “ALPHA” + “R” + “X2“+ “ALPHA” + “H” + “STO” + “ALPHA” + “V”. Press “ENTER” to save the expression and store it as a new variable.
• Press “PRGM” and go to “3: DISPLAY” to write the name of a new variable.
• Press “2ND” + “ALPHA.” Start with the quotations. Type “VOLUME.” Put the alpha lock off. Please note that a program name can contain at least one letter and no more than eight letters.
• Go to the “PRGM EXEC” menu to see the names of the stored programs.
• Select “CYLINDER” and press “ENTER.”
• To execute this program, press “ENTER.” You need to enter the values of R (radius) and H (height) for the program to calculate the volume of a cylinder.
• Press “ENTER.” The text “VOLUME” and the calculated value of the volume are displayed.
• Please note that programs created with OS 2.43 may run incorrectly if you use a later version of OS. Test the programs created with earlier versions to ensure that they yield correct results.
• If you want to delete the program, press “2ND” + “MEM” and select “2: MEM MGMT / DEL”.
• Select “7:PRGM” from the program editor.
• After selecting the program which you want to delete, press “DEL.”
• Press “YES” to confirm that you want to delete this program.

## References

Chronological calculator timeline. (n.d.). Web.

Harris, K. (2019). It all adds up: The history of the calculator. Web.

National Museum of American History. (n.d.). Electronic calculators – Handheld. Web.

Williams, J. B. (2017). The electronics revolution: Inventing the future. Cham, Switzerland: Springer.

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