Abstract: A slope measurement and drawing aid (100) for teaching mathematics having unique indicia (130), rational-numeric slope values (184), and mathematical information (192), and a method of identifying the correct rational-numeric slope value associated with the graph of a given line, either by means of a gravity-activated indicator arm (140), or by means of the orientation of the teaching aid. For instructional purposes, when used in a classroom setting, the teaching aid can be removably held on a vertical board by magnetic (240R) or other means. When used in an individual setting, a smaller version of the teaching aid can similarly be used in a horizontal orientation on paper.

Abstract: 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.

Abstract: A system and method for generating a test and an answer key to identify correct answers is disclosed. A test can be created by entering a set of questions with answer choices and correct answers at the same time. The tests can be rendered via a rendering device that includes both the questions and the answer choices. A ticket can be generated that drives a CNC (computer numerically control) machine to create a punched answer key with holes that align over correct answers. The answer key can also be rendered on a transparency utilizing a solid color everywhere except an area where the correct answer should be marked. The test and the answer key can also be rendered and aligned side by side in order to identify correct answers.

Abstract: The present invention provides a teaching aid system (10) for assisting students in applying trigonometric classroom lessons in real life applications both in indoor and outdoor settings. The teaching aid system consists of a pivoting scope (16) and an asymmetrically weighing gravity dial (18) that are pivotally mounted to a pair of support members (12). A tape measure (42) and an arithmetic electronic calculator (46) are attached on the support members (12) to enable students compute trigonometric formulations and applications of the same, when utilizing the system for real life objects either in indoor or outdoor settings. For determining dimensions of viewed objects, the student determines the distance from the viewed object using the tape measure (42), and the angles between the top and bottom of the viewed object using the scope (16) and gravity dial (18).

Abstract: An apparatus for displaying or measuring a trigonometric sine or cosine is provided, which includes a planar surface with a circle or a portion thereof and a bisecting line through the center of the circle. Two arms are attached to the apparatus. The circle, bisecting line and second arm include incremental markings that correspond to the degree and/or radian measurements of the unit circle, trigonometric cosine and trigonometric sine, respectively. A method is also provided which includes rotating one of the arms to a position along the circle to form an angle. Based upon the position of the first and second arms the trigonometric cosine and trigonometric sine of the angle can be read. An electronic display device that displays the trigonometric sine and trigonometric cosine of an angle can also be included.

Abstract: A device that teaches the relationship between a cylinder's surface areas and volume, its diameter and radius, the top circle circumference and area, the arc length, the sector area, the volume of a slice, the front area of the slice and the side area of the slice. The device includes a transparent hollow outer half-cylinder, and a solid inner half-cylinder that can rotates around a common center for both the inner and outer half-cylinders. The outer half-cylinder has marked off units around the 180 degrees of the half-cylinder. The equations of arc length and sector area along with examples of their meanings are shown on the top half circle. The inner half-cylinder also has marked off units around the 180 degrees of the half-cylinder. The equations for volume of a slice, the front surface area of the slice, and the side surface area of the slice are shown.

Abstract: The invention is an educational demonstration designed to help students better understand the concepts of torque and the inverse square law. A variable torque pulley consists of a rigid overlapping spiral shape member and a rigid circular member. The circular member is attached to the spiral shaped member as one integral piece, each incorporating a groove around the perimeter to act as a guide for a length of string. The circular member acts as a pulley and the spiral shape member acts as a lever. The variable torque pulley rotates in a circular fashion pivoting on an axle about its center. String is used with the circular member to rotate the apparatus. String is used with the spiral shape member for the hanging of a weight. The axle acts as the fulcrum for the spiral shape member. The shape of the spiral is important because as the variable torque lever rotates, the weight moves toward the fulcrum and the torque drops off in harmony with the inverse square law.

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: The location recorder assembly consists of a pair of disks, each bearing location site information about their periphery. The disks are held together by a pair of indicator studs, the heads of which are independently rotatable and which bear designation devices to permit a particular location site to be designated by the rotational orientations of the disks and the indicator studs.

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 toy useable to teach elementary mathematics to children includes a spaced series of mutually aligned parallel rods secured in a side-by-side relationship at their opposite ends to a base portion of the toy. Series of counting beads are captively and slidably mounted on all but two of the rods for movement between their opposite end portions. The remaining two rods, each of which has at least one counting bead rod on each of its opposite sides, slidably carry two operational sign beads having convex polygonal cross-sections. Different equation operation sign indicia are suitably positioned on the flat exterior side surfaces of the sign beads such that they can be rotated about their rods to display selected operational signs to the user of the toy.

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 demonstrative teaching apparatus for teaching the relationship between variable pictorial and/or graphic displays and their respective numerical values, in which the entire apparatus is positioned within an apparatus housing. The apparatus housing incorporates viewing areas on its front and rear sides so as to provide optical display of the relevant teaching portions of the apparatus. The front viewing area reveals the position of the segmented display while the rear viewing area reveals numerical indicia corresponding to the display of segments appearing through the first viewing area. The segmented display and, in turn, its respective numerical indicia, can be increased or decreased by forward or reverse rotation of a circular disk. The circular disk is precluded from excessive rotation in either direction through stopping mechanisms which limit the inadvertent winding or unwinding of the segmented display.

Abstract: A visual aid in which a background sheet, FIG. 1, features a diagram. It is desired to demonstrate that one part of the diagram, in this case the angle ACD can fit exactly on another part, in this case the angle ABC. The two parts are jointly used as the basis of a geometrical construction to locate the position of the center of rotation P. A transparent sheet (FIG. 2) is laid over the background sheet. The point Q is marked corresponding to P and the two sheets are pivotally assembled through P and Q. The relevant part of the background diagram, in this case the angle ACD is now copied onto the overlay sheet, in this case angle G. Pivotal movement of the overlay sheet will allow angle G to be alternately superimposed on angles ACD or ABC. The tongue T, fits in the slot S to limit the pivotal movement.

Abstract: FIG. 5 shows a background sheet A featuring the axes X and Y. A transparent strip E is pivotally assembled to A at the pivot point O. A transparent flat tube F is slidable on E. A straight line D is drawn on E and F through O. An operating button G is attached to F. A transparent cover sheet H is placed over the assembly. A small gap K is left between A and H by means of the distance pieces L. A slot J in the cover sheet H provides access to G. The axes may be calibrated to represent any entities involved in linear relationships, such as percentages, elements of multiplication, division etc. The gradient of the line D may be varied manually, thereby illustrating varying rate of proportionality.

Abstract: An educational entertainment device includes at least one cube formed from (a) a regular tetrahedron and (b) four 1/8th sections of a regular octahedron wherein the faces of the tetrahedron and the faces of the octahedron are all congruent. The 1/8th sections are formed by slicing the octahedron through three orthogonal planes, each slicing plane passing through four vertices of the octahedron, each 1/8th section being defined by (a) one octahedron face and (b) three mutually orthogonal corner faces. By coupling the octahedron face of each of the four 1/8th sections to a corresponding one of the tetrahedron faces in edge-to-edge fashion, one cube is formed. Each side of the cube includes two corner faces, one from each of two 1/8th sections. By rotating a 1/8th section about an axis perpendicular to the plane interfacing the 1/8th section and the tetrahedron, the two corner faces forming a cube side can be altered. A plurality of n.sup.3, e.g. eight, cubes can form a block of cubes, in an n.times.n.times.

Abstract: A transparent face plate has inscribed thereon a first circle surrounded by graduations which divide it into zero through 360.degree.. Two lines of transparency, which are denoted sine and cosine, respectively, intersect at right angles at the center of the circle, and at opposite sides of the center are divided into decimal graduations 0.01 through 1.0. Mounted to rotate beneath the base plate is a disc having inscribed on its face an indicator circle having a radius equal to one half of that of the first-named circle, and located in offset relation to the latter, so that the indicator circle extends at one diametral side through the center of the first circle, and at its opposite diametral side registers tangentially with said first circle.