Trigonometric Display Clock Using Rotating Secondary Circle
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing visualizations of trigonometric functions, such as triangles and shapes, are limited in effectively communicating mathematical information, necessitating additional methods to depict these functions clearly.
Innovation Solution
A trigonometric function display clock is designed with a unit circle and a secondary circle that rotates about a central axis, allowing the secondary circle to intersect with axial markings to determine values of sine and cosine functions, with the secondary circle being coupled to clock hands to visualize these functions dynamically.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If traditional triangles and shapes are used to depict trigonometric functions, then the visualization is simple to create, but the effectiveness in communicating mathematical information is limited
Solution Approach 1:
The patent combines a clock mechanism with trigonometric function visualization by integrating the secondary circle, axial markings, and clock hands into a single display system. The clock hands rotate to dynamically indicate sine and cosine values on the unit circle, merging time-telling functionality with mathematical visualization to enhance information communication without requiring separate displays
Solution Approach 2:
The patent employs dynamic rotation of the secondary circle and clock hands to continuously display changing trigonometric values. As the hands rotate around the clock face, they dynamically indicate different sine and cosine values at various angles, transforming static geometric shapes into an active, information-rich visualization system
2Loss of information
If a secondary circle is added to visualize trigonometric functions dynamically, then the visualization effectiveness is improved, but the device complexity increases
Solution Approach 1:
The secondary circle serves multiple functions simultaneously: it acts as the boundary of the unit circle for trigonometric visualization, provides the scale for measuring angles and trigonometric values, and serves as the rotation path for clock hands. This multi-functionality reduces the need for separate components, thereby limiting the increase in device complexity while maintaining enhanced visualization capability
Solution Approach 2:
The patent adds the dimension of rotational motion to traditional static trigonometric displays. By rotating the secondary circle and clock hands through angular displacement, the system visually represents trigonometric functions as dynamic projections, transforming a two-dimensional static diagram into a three-dimensional rotating display that enhances comprehension
3Adaptability or versatility
If clock hands are coupled to the secondary circle, then time display and trigonometric visualization occur simultaneously, but the operational complexity increases
Solution Approach 1:
The clock hands are directly coupled to the secondary circle mechanism, merging the time-telling function with trigonometric visualization. The same rotational motion that indicates time on a clock face simultaneously displays sine and cosine values, eliminating the need for separate operation mechanisms and maintaining ease of use while achieving dual functionality
Data Source
AI summary
A trigonometric function display clock includes a clock face that has a center aligned with a central axis, axial markings aligned with an x-axis and a y-axis, and a secondary circle having a diameter equal to a radius of the axial markings. A first point on the secondary circle is aligned at the center of the central axis, and the secondary circle is configured to be rotatable about the first point. The secondary circle is configured to overlap and align with at least a portion of the axial markings as the secondary circle rotates about the first point.