Abstract:
An adjustable device to locate and transfer the positions of golden section points from a source image to a secondary surface, comprising a plurality of paired blades that are coupled to pivot at the golden section points that occur along the length of the blades and at the endpoints of the blades. This configuration creates a looped series of connected levers, sequenced to diminish in length by golden section ratio, with fulcrums positioned at golden section points. The device is bilaterally symmetrical and maintains consistent golden section proportions regardless of the size to which it is adjusted. The creation of accurate images by a means other than tracing enables the user to learn how the mathematics of the golden section relates to the principles of proportion that connect the parts to the whole.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS:  
       [0001]     This application claims the benefit of provisional patent application Ser. No. 60/677,184 filled 2005 May 2 by the present inventor. 
     
    
     FEDERRALLY SPONSORED RESEARCH  
       [0002]     None  
       SEQUENCE LISTING  
       [0003]     None  
         [0004]     1. Field of Invention  
         [0005]     This invention relates to a novel device that provides artists and designers with a means to create works that accurately articulate the dynamics of proportion found in nature.  
         [0006]     2. Background of Invention  
         [0007]     There have been numerous attempts to provide a coherent system to allow for an improved way to accurately render the human body. A method for measuring the physical attributes of the human body proposed by Leonardo DaVinci is referenced by Curtin, U.S. Pat. No. 4,823,476, Apr. 25 1989. Curtin provides a static transparent panel that divides the body into predetermined segments. The invention fails to provide an adjustable means of measuring and transferring the details of proportion that are intrinsic to the golden section.  
         [0008]     U.S. Pat. No. 5,174,037, Dec. 29, 1992, Curtin provides a similar method for measuring the human head. This is also a static grid that fails to disclose the golden section.  
         [0009]     U.S. Pat. No. 1,280,094, Sep. 24, 1918, Smith describes a method for rendering the human body and head by presenting a grid divided into various-sized diamond shapes. The invention is static and there is no disclosure of the golden section.  
         [0010]     U.S. Pat. No. 2,780,004, Mar. 25, 1954, Rosenbaum describes a method for measuring the human head in relation to providing eyeglasses. The device comprises a frame with movable blades that can be aligned to specific features of individual faces. The device is limited to the face and presents no understanding of the golden section.  
         [0011]     U.S. Pat. No. 1,462,850, Jul. 24, 1923, Clark describes a profile-defining apparatus. This device provides a series of adjustable components that feature a number of various geometrical possibilities that can be combined to create assorted profiles. There is no disclosure of the golden section.  
         [0012]     U.S. Pat. No. 364,043, May 31, 1887, Riche describes an improved pantograph. Riche&#39;s device allows for an image to be reduced or enlarged in a manner that can also flip the image on its X axis. The 4 bars of his invention must be attached to a guide track. They are coupled at predetermined points that ignore the principles of the golden section.  
         [0013]     U.S. Pat. No. 4,397,090, Aug. 9, 1983, Nicyper describes an improved pantograph that allows for the image being copied to be re-proportioned and/or reversed. To manifest this feature, the 4 bars of his device can be coupled at points that are adjustable. The guide track is also adjustable. Nicyper does not disclose the use of the golden section.  
         [0014]     U.S. Pat. No. 834,470, Oct. 30, 1906, Hanssen describes an improved pantograph comprising a triangular frame from which a series of intermediate arms are attached in two sets of equal numbers. The value of each subsequent endpoint increases in intervals of 400. There is no mention of the golden section.  
         [0015]     U.S. Pat. No. 3,562,919, Aug. 29, 1968, Green describes a device comprising four arms of a movable parallelogram with one comer attached to a fixed blade featuring a protractor and the opposite comer being confined to move along a straight edge. The device is utilized as a layout tool for a machine shop. There is no relationship to the golden section disclosed.  
         [0016]     U.S. Pat. No. 5,867,588, Feb. 25, 1989, Marquardt describes a grid to be placed over an image of the human face for the purposes of facial identification and to determine what constitutes beauty. Marquardt discloses a grid composed of interrelated pentagons and five-pointed stars. Points along the grid are then correlated with various aspects of individual facial features. This process reflects back to DaVinci&#39;s understanding of man&#39;s relationship to the five-pointed star exemplified in the famous drawing of a man inscribed in a five-pointed star with his limbs outstretched within the circumference of a circle. The golden section is intrinsic in the structure of the pentagon and the five-pointed star. Marquardt is able to correlate positions of the disclosed grid with the golden section for this reason. His invention is static and only applicable to a frontal view of the human face.  
         [0017]     The golden section refers to a well-established mathematical ratio that relates segments of different sizes to each other. The golden section is the division of a line into two parts where the smallest part of the line is to the largest part of the line as the largest part of the line is to the entire line. If the line in question were to be divided in half, the decimal equivalent would be 0.5. The decimal equivalent of the golden section is 0.618. The square root of five, minus one, divided by two, also expresses its value. A remarkable property of this number is demonstrated by the following two equations: 1/0.618=1.618 and 1+0.618=1.618. Add 0.618 to one, or divide one by 0.618, either way you get the same answer.  
       SUMMARY OF INVENTION  
       [0018]     To successfully render a life-like image of a person&#39;s face, the position and proportion of their individual features are of extreme importance. Comparing the work of those who are skilled in this art with those who are not provides a means of discerning which configurations are the most problematic. The relative size, shape and placement of the eyes, nose and mouth are among the most common errors. Comparable inconsistencies of proportion and position can be observed in renderings of the entire human body.  
         [0019]     What is needed is a device that will assist a user of this device in correctly placing the subject&#39;s individual features in the proper proportion and position. The present invention provides the users with a novel device and an effective way to increase the accuracy of their renderings in addition to teaching about the mathematics of proportion that are found in the golden section.  
         [0020]     The device also teaches about the mathematical ratio first presented by Archimedes who once said, “Give me a lever long enough and a place to stand and I could lift the world.” The lever and fulcrum are an example of a simple machine. Archimedes also said, “The ratio of the weight moved to the weight moving it is the inverse ratio of the distances from the center.” The placement of the fulcrum determines the amount of force needed to move the lever. If the fulcrum is located at the half-way point of the lever, 0.5, then the force applied will be equal to the force released.  
         [0021]     As the distance between the fulcrum and the force applied increases, then the force necessary to move the lever decreases in a ratio that is consistent with the distance moved, causing the speed of the procedure to slow down. If the fulcrum moves closer to the force applied then more force is needed and the speed of the action is increased.  
         [0022]     The construction of the device of the present invention utilizes the ratio of the golden section combined with the principle of the simple machine known as a fulcrum and lever, whereby the position of the fulcrum will be located at the golden section point, 0.618.  
         [0023]     Because the present invention can be articulated from either end, it is possible to demonstrate how the placement of the fulcrum creates two separate dynamics. When using the device from the end that features eyelet  22 , the fulcrum is at a distance greater than halfway. When using the device from the end that features eyelet  33 , the fulcrum is at a distance closer than halfway. This understanding can be applied when adjusting the size of the device.  
         [0024]     Accordingly, it is the object of the invention to provide an adjustable tool to indicate the presence of the golden section in both the creations of nature and the designs of mankind.  
         [0025]     It is another object of the invention to provide a device that is able to accurately determine the size and relative position of the various features that determine the appearance of an individual human face, and transfer that information from a source image to a secondary surface.  
         [0026]     It is also an object of the invention to determine, with accuracy, the size and relative position of the various features that determine an individual human body, and transfer that information from a source image to a secondary surface.  
         [0027]     It is a further object of the invention to provide a device that can be adjusted to a compact size that can be carried in one&#39;s pocket and provide the fimctions mentioned above.  
         [0028]     Still another object of the invention is to provide a useful tool that is easy to operate and inexpensive to manufacture.  
         [0029]     Yet another object of the invention is to provide a tool that enables the user to study the principles demonstrated by a looped series of connected levers, sequenced to diminish in length by golden section ratio with fulcrums positioned at golden section points.  
         [0030]     It is also an object of the invention to provide designers of jewelry, furniture and other man-made objects with a means to proportion parts of their creations in accordance with the natural ratios of the golden section.  
         [0031]     Another object of the invention is to provide plastic surgeons and other doctors and dentists who practice corrective medical procedures with a device to aid them in the process of reconfiguring misaligned features in accordance with the golden section.  
         [0032]     It is also an object of the invention to provide artists and designers with a tool to create abstract and ornamental images that incorporate the golden section.  
         [0033]     An additional object of the invention is to provide a tool that allows for the construction of pentagons and five-pointed stars, circles, parallelograms, regular polygons and the regular stars associated with them.  
         [0034]     Yet another object of the invention is to provide a tool for scientists to examine the components of matter for configurations that provide examples of the golden section.  
         [0035]     Still another object of the invention is to provide a useful tool for design engineers to create more effective vehicles and machines that make use of the golden section.  
         [0036]     It is also an object of the invention to provide engineers with a looped series of connected levers, sequenced to diminish in length by golden section ratio with fulcrums positioned at golden section points, to provide a means to allow for the creation of more efficient machines.  
         [0037]     Another object of the invention is to provide biologists with a method for examining various life forms for examples of the golden section.  
         [0038]     One other object of the invention is to provide a tool that can be modeled into a digital version for individuals who utilize computers in the methodology of their creations.  
         [0039]     The present invention is an adjustable device for locating golden section points. In addition to identifying the location of golden section points, it also provides a means to transfer this information from a source image to a secondary surface. The invention is comprised of a plurality of paired blades that diminish in length by a ratio that is consistent with the golden section.  
         [0040]     The blades are coupled to pivot at golden section points that occur along the length of said blades and at the endpoints of said blades. This configuration provides a looped series of connected levers, sequenced to diminish in length by golden section ratio, with fulcrums positioned at golden section points.  
         [0041]     The blades are coupled with eyelets that allow for a marking implement to score the surface on which the device rests. The device is bilaterally symmetrical and maintains consistent golden section proportions regardless of the size to which it is adjusted.  
         [0042]     One way to utilize the present invention requires that it be placed directly on the surface of a source image and adjusted so that the area defined by the inner circumference of two eyelets corresponds with two positions on the source image. This process of adjustment is called tuning; it sets the device to be in sync with the specific geometry of the image. Pulling the top corner, eyelet  22 , and the bottom corner, eyelet  33 , apart will lengthen the invention, and pushing them together will cause the device to contract.  
         [0043]     If, for example, the subject in question is a face, the pupils of both eyes are suggested locations for alignment, as seen in  FIG. 3G . However, any two points can be applied to effectively utilize the invention. Once the pupils have been set, the device is considered tuned and it can be moved to another surface and placed in the location where the new image is to be rendered.  
         [0044]     The invention now functions as a template for a pointed implement to make marks that correspond to each pupil. As an example, in  FIG. 3G  the center of eyelet  25  marks the location of the left pupil, and the center of eyelet  26  marks the location of the right pupil.  
         [0045]     The secondary surface now has two marks indicating the location of the right and left pupils as they appeared in the source image.  
         [0046]     Return the invention to the source image and rotate it 180 degrees so the same two eyelets are still aligned to the pupils,  FIG. 3H , only now eyelet  26  will correlate with the left pupil and eyelet  25  with the right pupil. This rotation will provide new points that then can be transferred as mentioned above.  
         [0047]     If the points that have been transferred are not considered sufficient to complete the secondary image, the user can return the invention to the source image and tune it to another configuration that will facilitate the transfer of additional points.  
         [0048]     The device can be utilized horizontally, vertically, or anywhere in between to locate new points on the source image.  
         [0049]     In the preferred embodiment, the blades are transparent to allow for greater visibility of the source image. This process of locating and transferring points is not limited to faces and can be applied to the entire body, or individual parts of the body, as well as other subjects both natural and man made. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0050]      FIG. 1  shows the device expanded to more than twice its smallest size.  
         [0051]      FIG. 1A  shows the device fully expanded.  
         [0052]      FIG. 1B  shows the device fully compacted.  
         [0053]      FIG. 1C  shows the device in a position between  FIG. 1  and  FIG. 1B .  
         [0054]      FIG. 2  shows a winged male ant known as Mutilla europea with the device tuned to the length of his wingspan, with eyelet  22  at the tip of the left wing and eyelet  33  at the tip of the right wing.  
         [0055]      FIG. 2A  shows the device still tuned to the configuration shown in  FIG. 2 , but flipped horizontally. The middle parallelogram formed by eyelet  27 , eyelet  35 , eyelet  28 , and eyelet  36  coincides with the parameters of the ant&#39;s thorax.  
         [0056]      FIG. 2B  shows the device still tuned to the wingtips of  FIG. 2 . The back and of the ant&#39;s head is marked by eyelet  32 , and the front of his head is defined by eyelet  31 . The edge of his left wing coincides with eyelet  26 , and eyelet  30  indicates the beginning of his right front leg.  
         [0057]      FIG. 2C  shows the device still tuned to the wingtips of  FIG. 2 . The beginning of the ant&#39;s abdomen is indicated by eyelet  25 , and it terminates at eyelet  26 .  
         [0058]      FIG. 2D  shows the device in another tuning. It is set so that eyelet  29  and eyelet  30  align to the ant&#39;s eyes.  
         [0059]      FIG. 2E  shows the device tuned as it was in  FIG. 2D . The length of the ant is defined by eyelet  34  at the tip of his head and eyelet  33  at the rear of his abdomen. The top edge of his left wing is marked by eyelet  25 . Eyelet  26  coincides with the top edge of his right wing. The thorax and abdomen join at eyelet  35 . The edges of an abdominal segment are defined by eyelet  27  and eyelet  28 .  
         [0060]      FIG. 2F  shows the device still set to the eyes of  FIG. 2D  but rotated  180  degrees on its Y axis. The back of the abdomen is marked by eyelet  22 ; eyelet  34  appears where the abdomen joins the thorax. The front tip of his head is eyelet  35 . The top edges of the left and right wings are marked by eyelet  25  and eyelet  26 .  
         [0061]      FIG. 2G  shows the device tuned to the pair of points that defme the length of the ant&#39;s body. It is set to align with the tip of the head, eyelet  22 , and the rear of the abdomen, eyelet  33 . An abdominal segment is defined by eyelet  27  and eyelet  28 . These two points are also consistent with the last division of the ant&#39;s rear legs.  
         [0062]      FIG. 3  shows the device placed horizontally on a woman&#39;s face and tuned to the pupils, eyelet  34  and eyelet  35 .  
         [0063]      FIG. 3A  shows the device tuned as it was in  FIG. 3 . The parameters of the right eye are defined by eyelet  31 , eyelet  33 , eyelet  32 , and eyelet  37 .  
         [0064]      FIG. 3B  shows the device tuned as it was in  FIG. 3 . The pupil of the right eye is eyelet  31 . The upper lid of the right eye is defined by eyelet  37 , eyelet  32 , and eyelet  33 .  
         [0065]      FIG. 3C  shows the device tuned as it was in  FIG. 3 . The nostrils are defined by eyelet  33  and eyelet  37 , the lower edge of the left ear by eyelet  35 .  
         [0066]      FIG. 3E  shows the device tuned as it was in  FIG. 3  but rotated vertically. The right lower eyelid is defined by eyelet  25  and eyelet  26 . The edge of the right jaw line coincides with eyelet  30 .  
         [0067]      FIG. 3F  shows the device set as in  FIG. 3  rotated 45 degrees. The right eyebrow is divided by eyelet  28 , eyelet  35  aligns with the right pupil, and eyelet  23  marks the left lower jaw line.  
         [0068]      FIG. 3G  tunes the device to align with the left pupil, eyelet  25 , and the right pupil, eyelet  26 . The middle of the bottom of the upper lip is marked by eyelet  36 .  
         [0069]      FIG. 3H  shows the device tuned as it was in  FIG. 3G  and rotated 180 degrees. The jaw line is defined by eyelet  24 , eyelet  22 , and eyelet  23 . The left pupil is marked by eyelet  26  and the right pupil is marked by eyelet  25 .  FIG. 3J  shows the device tuned as it was in  FIG. 3G . The top of the upper lip is eyelet  33 , eyelet  37  marks the bottom of the nose, eyelet  27  the inner comer of the left eye and eyelet  28  is the inner comer of the right eye.  
         [0070]      FIG. 3K  shows the device tuned to the left pupil, eyelet  22 , and the right pupil, eyelet  35 .  
         [0071]      FIG. 3L  shows the device tuned as in  FIG. 3K . The comers of the left eye are defined by eyelet  34  and eyelet  35 . The inside comer of the right eye is marked by eyelet  37 . The upper right eyelid is eyelet  32 . The lower right eyelid is eyelet  33 .  
         [0072]      FIG. 3M  shows the device tuned as it was in  FIG. 3K . The right pupil is marked by eyelet  26 , and the outsides of the nostrils are defined by eyelet  22  and eyelet  34 . The right jaw line beneath the ear is eyelet  27 .  
         [0073]      FIG. 3N  shows the device tuned as it was in  FIG. 3K  and rotated 45 degrees. The right nostril is marked by eyelet  34 . The right comer of the mouth is defined by eyelet  22 . The left pupil is marked by eyelet  37 .  
         [0074]      FIG. 3P  shows the device tuned to the right pupil, eyelet  25 , and the left pupil, eyelet  26 . The middle of the bottom of the nose is marked by eyelet  22 .  
         [0075]      FIG. 3R  shows the device tuned as it was in  FIG. 3P . The nostrils are defined by eyelet  32  and eyelet  31 . At the top of the upper lip are eyelet  30  and eyelet  29 . At the bottom of the lower lip are eyelet  28  and eyelet  27 .  
         [0076]      FIG. 3S  shows the device tuned to the left pupil, eyelet  22 , and the right pupil, eyelet  35 . The right eyebrow starts at eyelet  26 . The right side of the head is marked by eyelet  33 .  
         [0077]      FIG. 3T  Shows the device tuned as it was in  FIG. 3S . The right pupil is eyelet  36 . The length of the device defines the area of both eyes, with eyelet  22  at the far comer of the left eye and eyelet  33  at the far comer of the right eye.  
         [0078]      FIG. 3U  shows the device tuned as it was in  FIG. 3S  rotated 90 degrees to a vertical position where the left pupil is marked by eyelet  36 . The left jaw line is eyelet  24 . The bottom of the top lip directly beneath the left nostril is eyelet  23 . The upper left eyelid coincides with eyelet  30  and eyelet  29 . The middle of left eyebrow is marked by eyelet  33 .  
         [0079]      FIG. 3V  shows the device tuned as it was in  FIG. 3S . The right pupil is eyelet  26 . The bottom of the nose directly between both nostrils is eyelet  23 . The right side of the face is eyelet  30  and eyelet  29 . The edge of the right ear is eyelet  31 .  
         [0080]      FIG. 4  shows the device over an image of a human skeleton tuned to the top of the skull, eyelet  22 , and to the bottom of the feet, eyelet  33 . The ankles align to eyelet  31  and eyelet  32 . The knees align to eyelet  27  and eyelet  28 . The wrists align to eyelet  25  and eyelet  26 . The shoulders align to eyelet  23  and eyelet  24 .  
         [0081]      FIG. 4A  shows the device tuned so that eyelet  32  links to the center of the right eye socket, and eyelet  31  links to the center of left eye socket.  
         [0082]      FIG. 4B  shows the device tuned to the alignment of  FIG. 4A . It reveals that eyelet  35  links to the left shoulder, eyelet  34 , to the elbow joint, eyelet  22 , to the finger tips of the hand, and eyelet  23  to the top of the right leg.  
         [0083]      FIG. 4C  shows the device tuned to the alignment of  FIG. 4A  rotated clockwise 90 degrees. The length of the right forearm is indicated by eyelet  27  and eyelet  28 .  
         [0084]      FIG. 4D  shows the device tuned to the alignment of  FIG. 4A  rotated counterclockwise 90 degrees. The length of the lower leg is indicated by eyelet  25  and eyelet  26 .  
         [0085]      FIG. 5  shows the device in the same position as in  FIG. 1  with the addition of four blades and twelve eyelets.  
         [0086]      FIG. 5A  shows the device of  FIG. 1  used as a template to create a five-pointed star. The points used to transfer the star are eyelet  22 , eyelet  26 , eyelet  23 , eyelet  24 , and eyelet  25 .  
         [0087]      FIG. 5B  shows the five-pointed star created by the points transferred from  FIG. 5A  by connecting eyelet  22  to eyelet  26  to eyelet  23  to eyelet  24  to eyelet  25  and back to eyelet  22 .  
         [0088]      FIG. 5C  shows the device of  FIG. 5  used as a template to create another five-pointed star. The points used to transfer the star are eyelet  22 , eyelet  41 , eyelet  44 , eyelet  39 , and eyelet  42 .  
         [0089]      FIG. 5D  shows the star created by the points transferred from  FIG. 5C  by connecting eyelet  22  to eyelet  41  to eyelet  44  to eyelet  39  to eyelet  42  and back to eyelet  22 .  
         [0090]      FIG. 5G  shows the device of  FIG. 5  used as a template to create yet another five-pointed star. The points used to transfer this star are eyelet  22 , eyelet  38 , eyelet  47 , eyelet  49 , and eyelet  45 .  
         [0091]      FIG. 5H  shows the star created by the points transferred from  FIG. 5G  by connecting eyelet  22  to eyelet  47  to eyelet  45  to eyelet  38  to eyelet  49  and back to eyelet  22 .  
         [0092]      FIG. 5J  shows the device as it was in  FIG. 1  with the protractor added to the end of blade  60  and blade  61 .  
         [0093]      FIG. 5K  shows blade  61 , eyelet  22  and eyelet  24 , isolated from the entire device. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0094]     The present invention provides an adjustable tool that combines principles of the golden section with a lever and fulcrum. The synergy of these two constants creates the unique and novel properties of the device. The invention is comprised of a plurality of paired blades that diminish in length by a ratio that is consistent with the golden section. The blades are coupled to pivot at golden section points that occur along the length of said blades and at the endpoints of said blades, providing a looped series of connected levers, sequenced to diminish in length by golden section ratio with fulcrums positioned at golden section points.  
         [0095]     The blades are coupled with eyelets that allow a marking implement to score the surface on which the device rests. The device is bilaterally symmetrical and the relationship of blades and eyelets maintains its golden section ratio regardless of the size to which the device is adjusted.  
         [0096]     The embodiments of the present invention are described with reference to the aforementioned drawings. Any modifications, variations or adaptations that rely upon the teachings of the present invention are considered to be within the scope and spirit of the present invention.  
         [0097]     As an example, the device set forth herein has been characterized as a tool to identify the golden section and to provide a guide to an individual wanting to use that information in the creation of a design or work of art, but it is apparent to those skilled in the art that the shape formed by the device in the compacted mode,  FIG. 1B , and its transformation to the shape formed by the device in its expanded mode,  FIG. 1A , that the present invention could be utilized as toy that provides the illusion of a growing Christmas tree.  
         [0098]     Hence, these descriptions and drawings are not to be considered in a limiting sense, as it is understood that the present invention is no way limited to the embodiments illustrated.  
         [0099]      FIG. 1A  shows the device as viewed from directly above. Blade  12  and blade  13  are of the same length. The length of blade  12  is determined by the location of the center of eyelet  23  on one end and the center of eyelet  26  on the other end. Blade  13  has a length that is determined by the location of the center of eyelet  24  on one end and the center of eyelet  25  on the other. Blade  12  and blade  13  are coupled to pivot by eyelet  34  so that blade  13  is on top of blade  12 . The location of eyelet  34  is determined by finding the golden section point for the length of blade  12  and the golden section point for the length of blade  13 .  
         [0100]     The golden section is determined by the location of the point that divides a segment of a fixed length into two parts, where the smaller part is to the larger part as the larger part is to the entire segment.  
         [0101]     The segment of blade  12 , determined by the placement of eyelet  26  and eyelet  34 , is to the segment of blade  12 , determined by the location of eyelet  34  and eyelet  23 , as the segment determined by the location of eyelet  23  and eyelet  34  is to the entire length of blade  12 . The segment of blade  13 , determined by the placement of eyelet  25  and eyelet  34 , is to the segment of blade  13 , determined by the location of eyelet  34  and eyelet  24 , as the segment determined by the location of eyelet  24  and eyelet  34  is to the entire length of blade  12 .  
         [0102]     Blade  10  and blade  11  are of the same length. The length of blade  10  is determined by the location of the center of eyelet  23  on one end and the center of eyelet  22  on the other end. Blade  11  has a length that is determined by the location of the center of eyelet  24  on one end and the center of eyelet  22  on the other. Blade  10  is the same length as the segment of blade  13 , determined by the location of eyelet  34  and eyelet  24 . Blade  11  is the same length as the segment of blade  12 , determined by the location of eyelet  34  and eyelet  23 .  
         [0103]     Blade  10  and blade  11  are coupled to pivot at their endpoints by eyelet  22  so that blade  10  is on top. Blade  10  is coupled to pivot to blade  12  by eyelet  23  so that it is on top of blade  12 . Blade  11  is coupled to pivot to blade  13  by eyelet  24  so that blade  13  is on top of blade  11 .  
         [0104]     Blade  14  and blade  15  are of the same length. The length of blade  14  is determined by the location of the center of eyelet  25  on one end and the center of eyelet  28  on the other end. Blade  15  has a length that is determined by the location of the center of eyelet  26  on one end and the center of eyelet  27  on the other.  
         [0105]     Blade  14  is the same length as the segment of blade  13 , determined by the location of eyelet  34  and eyelet  24 . Blade  15  is the same length as the segment of blade  12 , determined by the location of eyelet  34  and eyelet  23 . Blade  14  and blade  15  are coupled to pivot by eyelet  35  so that blade  15  is on top of blade  14 .  
         [0106]     The location of eyelet  35  is determined by finding the golden section point for the length of blade  14  and the golden section point for the length of blade  15 . The segment of blade  14 , determined by the placement of eyelet  28  and eyelet  35 , is to the segment of blade  14 , determined by the location of eyelet  35  and eyelet  25 , as the segment determined by the location of eyelet  25  and eyelet  35  is to the entire length of blade  14 .  
         [0107]     The segment of blade  15 , determined by the placement of eyelet  27  and eyelet  35 , is to the segment of blade  15 , determined by the location of eyelet  35  and eyelet  26 , as the segment determined by the location of eyelet  26  and eyelet  35  is to the entire length of blade  15 . Blade  14  is coupled to pivot to blade  13  by eyelet  25  so that blade  13  is on top of blade  14 . Blade  15  is coupled to pivot to blade  12  by eyelet  26  so that blade  15  is on top of blade  12 .  
         [0108]     Blade  16  and blade  17  are of the same length. The length of blade  16  is determined by the location of the center of eyelet  27  on one end and the center of eyelet  30  on the other end. Blade  17  has a length that is determined by the location of the center of eyelet  28  on one end and the center of eyelet  29  on the other.  
         [0109]     Blade  16  is the same length as the segment of blade  15  determined by the location of eyelet  35  and eyelet  26 . Blade  17  is the same length as the segment of blade  14  determined by the location of eyelet  35  and eyelet  25 . Blade  16  and blade  17  are coupled to pivot by eyelet  36  so that blade  17  is on top of blade  16 . The location of eyelet  36  is determined by finding the golden section point for the length of blade  16  and the golden section point for the length of blade  17 .  
         [0110]     The segment of blade  16 , determined by the placement of eyelet  30  and eyelet  36 , is to the segment of blade  14 , determined by the location of eyelet  36  and eyelet  27 , as the segment determined by the location of eyelet  27  and eyelet  36  is to the entire length of blade  14 .  
         [0111]     The segment of blade  17 , determined by the placement of eyelet  29  and eyelet  36 , is to the segment of blade  17 , determined by the location of eyelet  36  and eyelet  28 , as the segment determined by the location of eyelet  28  and eyelet  36  is to the entire length of blade  17 . Blade  16  is coupled to pivot to blade  15  by eyelet  27  so that blade  15  is on top of blade  16 . Blade  17  is coupled to pivot to blade  14  by eyelet  28  so that blade  17  is on top of blade  14 .  
         [0112]     Blade  18  and blade  19  are of the same length. The length of blade  18  is determined by the location of the center of eyelet  32  on one end and the center of eyelet  29  on the other end. Blade  19  has a length that is determined by the location of the center of eyelet  31  on one end and the center of eyelet  30  on the other.  
         [0113]     Blade  18  is the same length as the segment of blade  17  determined by the location of eyelet  36  and eyelet  28 . Blade  19  is the same length as the segment of blade  16  determined by the location of eyelet  36  and eyelet  27 . Blade  18  and blade  19  are coupled to pivot by eyelet  37  so that blade  19  is on top of blade  18 . The location of eyelet  37  is determined by finding the golden section point for the length of blade  18  and the golden section point for the length of blade  19 .  
         [0114]     The segment of blade  18 , determined by the placement of eyelet  32  and eyelet  37 , is to the segment of blade  18 , determined by the location of eyelet  37  and eyelet  29 , as the segment determined by the location of eyelet  29  and eyelet  37 , is to the entire length of blade  18 .  
         [0115]     The segment of blade  19 , determined by the placement of eyelet  31  and eyelet  37 , is to the segment of blade  19  determined by the location of eyelet  37  and eyelet  30 , as the segment determined by the location of eyelet  30  and eyelet  37  is to the entire length of blade  19 .  
         [0116]     Blade  18  is coupled to pivot to blade  17  by eyelet  29  so that blade  17  is on top of blade  18 . Blade  19  is coupled to pivot to blade  16  by eyelet  30  so that blade  19  is on top of blade  16 .  
         [0117]     Blade  20  and blade  21  are of the same length. The length of blade  20  is determined by the location of the center of eyelet  33  on one end and the center of eyelet  31  on the other end. Blade  21  has a length that is determined by the location of the center of eyelet  33  on one end and the center of eyelet  32  on the other.  
         [0118]     Blade  20  is the same length as the segment of blade  19 , determined by the location of eyelet  37  and eyelet  30 . Blade  21  is the same length as the segment of blade  18  determined by the location of eyelet  37  and eyelet  29 . Blade  20  is coupled to pivot to blade  19  by eyelet  31  so that blade  19  is on top of blade  20 . Blade  21  is coupled to pivot to blade  18  by eyelet  32  so that blade  21  is on top of blade  18 .  
         [0119]      FIG. 5  shows another embodiment of the invention seen in  FIG. 1  providing four additional blades and twelve additional eyelets. It conforms to the same parameters established for  FIG. 1 .  
         [0120]     Blade  50  is coupled to blade  10  by eyelet  44  at one end and coupled to blade  13  by eyelet  41  at the other end. Blade  53  is coupled to blade  10  by eyelet  45  at one end and coupled to blade  13  by eyelet  40  at the other end. Blade  51  is coupled to blade  11  by eyelet  38  at one end and coupled to blade  12  by eyelet  43  at the other end.  
         [0121]     Blade  54  is coupled to blade  11  by eyelet  39  at one end and coupled to blade  12  by eyelet  42  at the other end.  
         [0122]     Blade  50  is coupled to blade  51  by eyelet  49  and to blade  54  by eyelet  48 . Blade  53  is coupled to blade  51  by eyelet  46  and to blade  54  by eyelet  47 . Eyelet  44  is the golden section point of eyelet  22  and eyelet  23 . Eyelet  45  is the golden section point of eyelet  22  and eyelet  44 . Eyelet  39  is the golden section point of eyelet  22  and eyelet  24 . Eyelet  38  is the golden section point of eyelet  22  and eyelet  39 .  
         [0123]     Eyelet  41  is the golden section point of eyelet  24  and eyelet  34 . Eyelet  40  is the golden section point of eyelet  24  and eyelet  41 . Eyelet  42  is the golden section point of eyelet  23  and eyelet  34 . Eyelet  43  is the golden section point of eyelet  23  and eyelet  42 .  
         [0124]     Eyelet  47  is the golden section point of eyelet  45  and eyelet  40 . Eyelet  46  is the golden section point of eyelet  45  and eyelet  47 . Eyelet  48  is the golden section point of eyelet  44  and eyelet  41 . Eyelet  49  is the golden section point of eyelet  44  and eyelet  48 . Blade  50 , Blade  51 , Blade  53 , and Blade  54  are the same size as Blade  14  and Blade  15 .  
         [0125]      FIG. 5J  shows the device with the addition of a protractor. The length of blade  60  is determined by the location of eyelet  23  and eyelet  22 . Eyelet  22  is located at the center of the circle that forms the protractor located at the end of blade  60 . The protractor is marked to denote 5 degree increments in a circle of 360 degrees. Blade  61  is coupled to pivot with blade  60  by eyelet  22  so that blade  60  is on top.  
         [0126]      FIG. 5K  shows blade  61  isolated from the device. Eyelet  22  appears in the center of the protractor circle that is marked by a line that is parallel to the edges of blade  61 . Eyelet  24  is located at the other end of blade  61 .