Line Division Device for Equal Sub-Parts
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Solution Overview
Problem
Existing geometric construction techniques, dating back to Euclid, are unable to universally divide a straight or curved line into any odd or even positive integer number of equal sub-parts, or by a prime number other than 2, due to limitations in subdividing arcs and angles.
Innovation Solution
A multi-part process and device with elongated flat members that can divide straight or curved lines into specified whole numbers of equal sub-parts, including odd and even numbers, and prime numbers, by attaching line ends to the flat members and wrapping the line around them to create equal length sub-parts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional Euclidean geometric construction techniques are used, then constructions can be performed with limited tools (compass and straightedge), but the ability to divide lines into any specified number of equal sub-parts is restricted
Solution Approach 1:
The device divides the line division task into sequential steps using multiple elongated flat members. Each member represents a segment of the division process, allowing the line to be divided into n equal parts by systematically wrapping and positioning the line around each member in sequence.
Solution Approach 2:
The device provides universal applicability by enabling division of lines into any specified number of equal sub-parts (n ≥ 2), including prime numbers and odd numbers, which were previously impossible with traditional Euclidean tools. The same device structure works for all integer divisions.
2Reliability
If Euclidean construction rules are followed, then geometric purity is maintained, but the ability to solve general line division problems (especially by prime numbers) is lost
Solution Approach 1:
The elongated flat members serve as intermediary elements that facilitate the division process. These members act as mediators between the line to be divided and the division process, enabling accurate division by any integer n through their physical geometry and the wrapping mechanism.
Solution Approach 2:
The invention replaces the abstract Euclidean geometric system with a concrete mechanical system using physical elongated flat members. This mechanical approach allows for the reliable division of lines into any number of equal parts through tangible manipulation and geometric constraints.
3Ease of operation
If simple geometric tools are used, then ease of operation is maintained, but the capability to divide lines into arbitrary numbers of equal parts is limited
Solution Approach 1:
The device incorporates dynamic elements through the wrapping process, where the line is systematically wrapped around multiple elongated flat members in sequence. This dynamic wrapping mechanism allows the same simple structure to handle any division number n by adjusting the number of members and wrapping pattern.
Solution Approach 2:
The invention adds a dimensional aspect by introducing multiple elongated flat members arranged in space, transforming the two-dimensional Euclidean plane into a three-dimensional configuration that enables arbitrary integer divisions through spatial arrangement and wrapping.
Data Source
AI summary
Multi-part processes and device with elongated flat members for line end-points, which together can divide a straight or curved line of unknown length into specified numbers of equal sub-parts. This invention significantly extends beyond the limited abilities of various devices and construction techniques, including geometric constructions used over millennia, to subdivide a line into equal sub-parts. The length of any straight-line in a plane can be subdivided into any specified positive natural number of equal sub-parts. The length of any 360° or less arc of a circle in a plane and its subtending central angle(s) can be subdivided into any specified positive integer number of equal sub-parts. Each of the four angles formed when two straight-lines intersect in a plane can be subdivided into any specified positive natural number of equal sub-parts. The specified number for subdivision may be any even or odd positive whole number, including a positive prime number. The multi-part processes and device can be used to produce definite specified fractional subdivisions of a line that are not equal sub-parts of the line. They may be applicable to subdividing arcs of constant curvature that are not circular. This invention can be used to avoid the abstractions in reality and illusions created when objects in the three-dimensional real world are represented two-dimensionally in a plane. The same applies to representations in three-dimensional constructions. This application is a continuation of patent application Ser. No. 16/580,542 in which the examiner found in an amended substitute specification that more than one invention had been disclosed.