Abstract: A method for designing a structure or the like is provided in which an arbitrary curve is approximately drawn using a circular segment. This method includes the steps of: setting a straight line which connects one end of a desired curve and the other end thereof; setting an intersection point of the curve and a perpendicular to the straight line at a middle point thereof; obtaining a distance between the intersection point and the middle point, and a length of a straight-line segment from each of the one end and the other end of the curve up to the middle point; setting a curvature radius of a circular segment which approximates the desired curve in association with these distance and length, and acquiring a radius center point of the circular segment; and setting a circular segment from the one end up to the other end of the curve by using this center point as the center thereof.

Abstract: A method for detecting an ellipsoid includes: extracting an ellipsoid candidate; extracting an ellipsoid contour; calculating an ellipsoid parameter; calculating an adaptability ratio; and eliminating the ellipsoid candidate. Extracting the ellipsoid candidate includes: inputting an image with figures; selecting the ellipsoid candidate from the figures; and extracting a contour candidate point and a center point. Extracting the ellipsoid contour includes: drawing straight lines; determining contour candidate points; calculating first and second distances; and defining ellipsoid contour points. Calculating the ellipsoid parameter is based on the ellipsoid contour points and the center point. Calculating the adaptability ratio includes: drawing a complete ellipsoid; and calculating the adaptability ratio between the complete ellipsoid and the ellipsoid candidate. Eliminating the ellipsoid candidate is performed when the adaptability ratio is equal to or smaller than a threshold.

Abstract: A method for designing an elliptical structure with an outline of an approximate elliptic curve, which is generated by connecting circular segments to one another, and an elliptical structure created on said method.

Abstract: A device that teaches the relationship between a circle, its diameter and its radius. The device includes a circular ring that has a rigid intersecting bar representing its diameter. Attachment mechanism allows flexible diameter bars to be attached around the outer perimeter of the circle. Flexible bars the same size as the diameter or the radius are available to attach to the outer perimeter by way of the attachment mechanism. Additional flexible bars are available at 0.14 diameters and 0.28 radiuses in length. When the flexible diameter bars are attached to the circle, three diameters bars and one 0.14 diameter bar are affixed around the circle's circumference representing 3.14 diameters. When the flexible radius bars are attached to the circle, six radius bars and one 0.28 radius bar are affixed around the circle's circumference representing 6.28 radius.

Abstract: A combination of devices that demonstrate visually and on an intuitive level mathematical principles relating to the circle including the number &pgr;, the relationship between circumference, diameter, radius and &pgr;, and the relationship between the area of a circle formed of circle sectors and an approximate parallelogram obtained by rearranging the circle sectors.

Abstract: The present invention provides a variety of laminated plastic activity boards that allow the individual to visualize and have interactive exploration of conic sections and their definitions. This allows for more class time to be spent investigating the concept of conic sections opposed to teachers lecturing and the students having to memorize them. The user is able to notice patterns which develop while drawing specific sets of conic sections by forming conjectures based on the observed outcomes of the activities. Each activity board has a reusable laminated surface which allows the ink used from a marker to be visible but not permanent. The surface can be wiped clean with a moist paper towel once the activity is completed. There are a total of four activity boards which operate independently of each other and contain different concepts. The four boards teach principles relating to the circle, ellipse, parabola and hyperbola.

Abstract: A method and apparatus for teaching a relationship of trigonometric functions between a unit circle and a rectangular coordinate system has a primary flexible member movable between a circular configuration defining the unit circle, and a straight configuration defining the rectangular coordinate system. A plurality of secondary linear members are removably coupled at attachment points along the flexible member. The linear members are movable with the flexible member between a unit circle position and a rectangular coordinate position. In the unit circle position, each linear member is oriented with respect to the unit circle to demonstrate and represent a trigonometric function. In the rectangular coordinate position, each linear member extends perpendicularly from the flexible member defining trigonometric wave forms. The flexible member and linear members physically represent the trigonometric functions and moving the members between the two systems demonstrates the relationship between them.

Abstract: A design for a circular, piece-matching math educational aid is disclosed. It contains a holding plate and various fraction pieces. The circular holding plate has a clockwise spiral bottom, designed in such a way that a sloped cliff is formed at the joint of the starting and ending point. The edge of the cliff is lined up with a guiding mark "0" on a fraction scale marked on an elevated wall on the outer circumference of the holding plate. The fraction pieces contain numerous pie-shaped segments. Any of the segments can precisely depict a fraction, based on the ratio of its center angle to the circle, 360 degrees. The pieces can be made with any center angles, such as 5, 7.5, 10, 30, 45, 60, 90, 180 degrees, etc.

Abstract: A visual aid teaching device for translating one or more superimposed picture images in a linear path at different positions with respect to a stationary underlay picture includes as basic components: a pair of edge strip members, each embodying two or more channel tracks; a transparent, or opaque, rectangular flat surface member snugly mounted on the edge strips through their channel tracks to assemble the body device; sets of layers, each including a stationary underlay picture member and one or more superimposed picture image members. Both members may include algebraic graphs or circles divided into sets of sectors. The layer members can be mounted on the other channel tracks. Algebraic problem solving of compound inequalities in one variable can be demonstrated algebraically along with their graphic solution sets simultaneously by means of translating one or more superimposed graphs at different positions with respect to a set of number line graphs.

Abstract: The pictorial image transforming manipulatives are instructional visual aid devices adapted for use to demonstrate visually the applications of deductive reasoning in proving most of the geometry theorems in conjunction with a geometry course. The manipulatives can also be used to display visually many graphs which represent algebraic linear equations and inequalities in two variables, and compound inequalities on a number line. These applications of mathematical systems for demonstrated algebraic linear graphs, and other graphs, are designed in conjunction with algebra textbooks.Each device uses one or more transparent overlays which rotate, translate, translate and rotate, flip over, or flip over and rotate to another position relative to a stationary underlaid plate. The manipulative devices are adapted for use on the overhead projector or for use in direct demonstration without a projector. These devices can be produced in small sizes for student use or in large blackboard sizes.

Abstract: An educational board for use in demonstrating mathematical principles has a surface marked with a circle having its circumference marked with gradations indicating 360 degrees. The board is provided with pins to mark any angular displacement along the circumference and connecting elastic bands which are stretched around the pins to create shapes inscribed in the circle.

Abstract: An electromechanical demonstrator board of one or more of the six trigonometric functions. The board is powered electrically by a battery and mechanically by a hand crank which drives a pointer and contact arm. The circuits include light emitting diodes (LEDs) arranged into three groups. The first group represents a unit circle. The second group is on a vertical segment, and the third group is on the path of the function and the horizontal axis. The first group of LEDs indicates particular angle measures on the unit circle. In the second group, vertically oriented LEDs indicate harmonic motion. The third group of LEDs demonstrates a graph of the trigonometric function and the measure of linear movement related to rotation on the unit circle.

Abstract: A signal measurement system with softkey menus for guiding a user in selecting a desired test setup, including selection and connection of the device to be tested, as well as selecting calibration measurement and test measurement for the device. In response to a given softkey selection, the signal measurement system prompts the user with a set of displayed textual instructions and pictorial diagrams via a user interface to step the user through setup, calibration, and measurement processes. Preferably, a signal processing unit (or analyzer) included in the signal measurement system incorporates the user interface in firmware to guide and aid the user in connecting the device to be tested to the signal measurement system for the desired test, and leading the user through calibration and measurement processes. The analyzer preferably displays the softkey menus, instructional text displays, and pictorial block diagram displays on a cathode ray tube included in the analyzer to guide the user.