Abstract: A method for path tracing of mathematical plots on a digital device is provided that includes receiving at least one mathematical expression on the digital device, and tracing a path of a plot of the at least one mathematical expression on a display screen coupled to the digital device, wherein tracing the path comprises displaying the path sequentially point by point as a value of an independent variable of the at least one mathematical expression changes over a domain of the independent variable.

Abstract: A method and a digital device for evaluating a generalized rational function are provided in which the evaluation of the generalized rational function includes computing all discontinuities of the generalized rational function, determining, for each discontinuity, whether or not the discontinuity is a removable discontinuity, wherein the determining includes determining whether or not the generalized random function approaches a point near the discontinuity, and displaying each removable discontinuity. A method for evaluating a generalized rational function on a handheld graphing calculator is provided that includes determining whether or not the generalized rational function has at least one asymptote and displaying the at least one asymptote on a display screen when the generalized rational function has the at least one asymptote.

Abstract: A method and a digital device for evaluating a generalized rational function are provided in which the evaluation of the generalized rational function includes computing all discontinuities of the generalized rational function, determining, for each discontinuity, whether or not the discontinuity is a removable discontinuity, wherein the determining includes determining whether or not the generalized random function approaches a point near the discontinuity, and displaying each removable discontinuity. A method for evaluating a generalized rational function on a handheld graphing calculator is provided that includes determining whether or not the generalized rational function has at least one asymptote and displaying the at least one asymptote on a display screen when the generalized rational function has the at least one asymptote.

Abstract: A method for path tracing of mathematical plots on a digital device is provided that includes receiving at least one mathematical expression on the digital device, and tracing a path of a plot of the at least one mathematical expression on a display screen coupled to the digital device, wherein tracing the path comprises displaying the path sequentially point by point as a value of an independent variable of the at least one mathematical expression changes over a domain of the independent variable.

Abstract: Disclosed embodiments relate to processing of gestures to cause computation of measurements of a line using a touch screen. A system includes a processor, a touch screen coupled to the processor, a gesture module coupled to the processor for executing a gesturing method. The method includes determining a gesture shape and whether the gesture shape selects a first line segment by intersecting the first line segment. When the gesture shape selects a first line segment, it is then determined whether the gesture shape also selects an additional line segment different from the first line segment. When an additional line segment is not selected, the method calculates the length measurement from the beginning point of the segment to the end point of the selected first line segment. The method further displays the length measurement on a display.

Abstract: Disclosed embodiments relate to processing of gestures to cause computation of measurements of a line using a touch screen. A system includes a processor, a touch screen coupled to the processor, a gesture module coupled to the processor for executing a gesturing method. The method includes determining a gesture shape and whether the gesture shape selects a first line segment by intersecting the first line segment. When the gesture shape selects a first line segment, it is then determined whether the gesture shape also selects an additional line segment different from the first line segment. When an additional line segment is not selected, the method calculates the length measurement from the beginning point of the segment to the end point of the selected first line segment. The method further displays the length measurement on a display.

Abstract: Described examples include a graphing device having a display. The graphing device also has a processor operable to present a graph of a function on the display and operable to generate a slider on the display in which at least one parameter of the slider is derived from a context element of the graph.

Abstract: Disclosed examples include drawing apparatus and methods of rendering lines on a display screen, in which a first angle is determined that corresponds to a hand drawn line created by a user on the display screen, and a new line is rendered on the display screen to represent the hand drawn line created by the user. The new line is selectively rendered parallel or perpendicular to an existing line on the display screen at least partially according to the first angle using the processor.

Abstract: Disclosed embodiments relate to processing of gestures to cause computation of measurements of a line using a touch screen. A system includes a processor, a touch screen coupled to the processor, a gesture module coupled to the processor for executing a gesturing method. The method includes determining a gesture shape and whether the gesture shape selects a first line segment by intersecting the first line segment. When the gesture shape selects a first line segment, it is then determined whether the gesture shape also selects an additional line segment different from the first line segment. When an additional line segment is not selected, the method calculates the length measurement from the beginning point of the segment to the end point of the selected first line segment. The method further displays the length measurement on a display.

Abstract: A method and a system for processing gestures to cause computation of measurements of an angle or a segment using a touch screen are disclosed. The system includes a processor, a touch screen coupled to the processor, and a gesture module coupled to the processor for executing a gesturing method. The method includes determining a gesture shape. For example, when the gesture shape is an arc or a line between two touching lines, the method calculates the measurement of the angle between the touching lines and behind the gestured line or arc. When the gesture is a line crossing a segment, the method calculates the measurement from the beginning of the segment to the end of the segment. The method further displays the calculated measurement of at least one of the angle or the segment.

Abstract: Disclosed examples include drawing apparatus and methods of rendering lines on a display screen, in which a first angle is determined that corresponds to a hand drawn line created by a user on the display screen, and a new line is rendered on the display screen to represent the hand drawn line created by the user. The new line is selectively rendered parallel or perpendicular to an existing line on the display screen at least partially according to the first angle using the processor.

Abstract: A method and a system for processing gestures to cause computation of measurements of an angle or a segment using a touch screen. The system includes a processor, a touch screen coupled to the processor, a gesture module coupled to the processor for executing gesturing method, the method includes determining a gesture shape, when the gesture shape is an arc between two touching lines, calculating the angle between the touching lines behind the gestured line or arc, when the gesture is a line crossing a segment, calculating the measurement from the beginning of the segment to the end of the segment, and displaying the calculated measurement of at least one of the angle or the segment.

Abstract: A system, method and device for forcing the measurement of a triangle. The method includes computing angles A B C, BAC and ACB for a triangle ABC, determining the measurement of at least one of angles ABC, BAC and ACB in degrees, nudging the angles to ensure that measurements are integers and add up to 180 degrees. The method may also include determining a closest integer to the measurement of the at least one of the angles ABC, BAC and ACB, rotating segment AC of the triangle ABC around A by a?-a degrees, where a is the measurement of the at least one of angles ABC, BAC and ACB and a? is the closest integer to the measurement of at least one of the angles ABC, BAC and ACB and wherein the new position of C is C? and angle BAC? is equal to a?, moving point C? along the fixed direction of line AC?, and ensuring that the other two the angles of the triangle ABC are integers.

Abstract: A graphical object is displayed on a display screen of a student device. The student device may then display one or more data elements pertaining to the graphical object on a display screen of the student device. An expression entered by the student may then be displayed on the display screen of the student device. Variables in the expression may be determined by parsing the expression. A sequence of prompts is presented by the student device to associate each of the variables of the expression with one of the data elements. In response to each prompt, a data element is selected and associated with a variable in response to user input to the student device.