Graph Display Method for Equation Verification
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Solution Overview
Problem
Conventional graphing scientific calculators lack the ability to visually indicate whether a modified equation is true or false relative to the original equation, limiting user understanding of the relationship between the two.
Innovation Solution
A method for displaying graphs corresponding to both original and modified mathematical expressions, where the display of a third graph indicates the correctness of the modified equation by visual differences such as color or overlay, based on matching or not matching solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If a text message or character icon is displayed to notify the user of whether a modified equation is true or false, then the notification function is achieved, but the visual relationship between the original equation and modified equation cannot be shown
Solution Approach 1:
The patent combines the notification function with the graph display function by overlaying visual indicators on the graphs themselves. The third graph (modified equation) is displayed together with the first and second graphs (original equations), and visual indicators such as color coding, line styles, or positioning show both the correctness of the modified equation and its relationship to the original equations simultaneously.
Solution Approach 2:
The patent transitions from one-dimensional text notification to two-dimensional graphical representation. By displaying the modified equation's graph in the same coordinate system as the original equations and using visual dimensions (color, position, overlay), the system conveys both correctness verification and relationship visualization in a single graphical interface.
2Loss of information
If only text messages are used to indicate correctness of modified equations, then the device complexity remains low, but the information conveyance capability is limited
Solution Approach 1:
The graph display system serves multiple functions simultaneously: it visualizes the original equations, displays the modified equation, verifies correctness through solution matching, and shows the relationship between equations. All these functions are achieved through the same graphical display mechanism, eliminating the need for separate text notification systems.
Solution Approach 2:
The patent uses color coding to indicate the correctness of modified equations and to differentiate between original and modified equations. For example, green color may indicate a correct modification while red indicates an incorrect one, and different colors can represent different original equations. This visual encoding conveys multiple pieces of information efficiently.
Data Source
AI summary
A graph display method, whereina first graph corresponding to a first mathematical expression is displayed on a display, andwhen an operation to input, as a modified expression of the first mathematical expression, a third mathematical expression having a notation different from that of the first mathematical expression is accepted, and a third graph corresponding to the third mathematical expression is displayed on the display, the third graph is displayed on the display in a way of displaying, the way being different depending on whether a condition that the first mathematical expression is mathematically identical to the third mathematical expression is satisfied or not.