WO1987001478A1 - A computer with an electronic mosaic of points in the solid of a tetrahedron - Google Patents

A computer with an electronic mosaic of points in the solid of a tetrahedron Download PDF

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Publication number
WO1987001478A1
WO1987001478A1 PCT/US1986/001805 US8601805W WO8701478A1 WO 1987001478 A1 WO1987001478 A1 WO 1987001478A1 US 8601805 W US8601805 W US 8601805W WO 8701478 A1 WO8701478 A1 WO 8701478A1
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WO
WIPO (PCT)
Prior art keywords
tetrahedron
solid
mosaic
computer
points
Prior art date
Application number
PCT/US1986/001805
Other languages
French (fr)
Inventor
Henry Merritt Farnum
Original Assignee
Henry Merritt Farnum
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from PCT/US1985/001670 external-priority patent/WO1987001408A1/en
Application filed by Henry Merritt Farnum filed Critical Henry Merritt Farnum
Priority to AU63729/86A priority Critical patent/AU6372986A/en
Publication of WO1987001478A1 publication Critical patent/WO1987001478A1/en

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Classifications

    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04H—BUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL
    • E04H3/00—Buildings or groups of buildings for public or similar purposes; Institutions, e.g. infirmaries or prisons
    • E04H3/10—Buildings or groups of buildings for public or similar purposes; Institutions, e.g. infirmaries or prisons for meetings, entertainments, or sports
    • E04H3/22—Theatres; Concert halls; Studios for broadcasting, cinematography, television or similar purposes
    • E04H3/24—Constructional features of stages
    • E04H3/26—Revolving stages; Stages able to be lowered
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations

Definitions

  • a PROBLEM IS A GEOMETRIC FIGURE
  • the Karmarkar algorithm takes a giant short cut, plunging through the middle of the solid. After selecting an arbitrary Interior point, the algorithm warps the entire structure—in essence, reshaping the problem—in a way designed to bring the chosen point exactly into the center. The next step is to find a new point in the direction of the best solution and to warp the structure again, bringing the new point into the center.
  • the long felt need is a method for use of a suitable solid, in a method which accurately represents an unlimited number of individual, relevant values or numbers, completely accurately in relation to every other "point" or "irregular bit of information" in the solid.
  • This invention describes the tetrahedron ara unique solid among the regular polygons, for many reasons includinn the following. Tetrahedron Structure (A Solid),
  • Fig, 1a shows four planes assembled into a three-dimensional solid, tetrahedron 32.
  • Fig, 1-a shows first plane MNO in a horizontal view. Its details not shown here were shown in Fig, 1-e, Plane MNO comprises seventh, eighth, and ninth girders 7, 8, and 9, and star I,
  • Fig, 1-a three additional planes are shown identical to said plane MN, said four planes comp rising a large triangle, plane MSP.
  • the second plane, NSV comprises first girder 27, second girder 28, and third girder 26, enclosing star y
  • Third plane CVP comprises first girder 31, second girder 29, and third girder 30, enclosing star VI
  • Said first, second, and third planes enclose fourth plane NVO, comprising first girder 7', second girder 8', and third girder 9', enclosing star I'.
  • Fig, 1-b shows a horizontal view of the structure shown in Fig, 1-a, with planes MNO, NSV, and OVP connected to construct a tetrahedron with its base comprising plane NVO, and with its apex designated U, Said planes are connected at a sixty degree angle in relation to each adjacent plane, by connectors (not shown)
  • any location in the mosaic of triangle ACE in its base is intersected by a line exactly perpendicular to the corresponding location in the mosaic of parallel plane WXY.
  • each equilateral plane within the mosaic of plane NVO comprising the base of tetrahedron 32 selectively may be constructed in a parallel plane connected to the corresponding locations of tetrahedron 32, In each mosaic thus constructed, it is apparent that each location is intersected by a Hne exactly perpendicular to the corresponding location in base NVO, within the solid comprising tetrahedron 32.
  • first plane MNO, second plane NSV, and third plane OVP comprise the surfaces of tetrahedron 32 shown in Fig. 1-b
  • Said three planes are identical to base NVO, Therefore any structural element connected to any said mosaic within the solid comprising tetrahedron 32, similarly may be connected to the corresponding locations within the irosalc comprising each of the said surfaces of tetrahedron 32.
  • tetrahedron 32 may be expanded to any order of magnitude, to comprise similar planes within its solid, and similar planes comprising its respective surfaces, with each respective mosaic of said Dlanes and surfaces characterized by the same features as tetrahedron 32, supra,
  • each surface of tetrahedron 32 is identical to its base NVO, Therefore tetrahedron 32 selectively may be rotated to establish any surface as its base, with its respective planes within said solid, and respective surfaces, characterized by the same features as tetrahedron 32, supra,
  • tetrahedron 32 expanded to any order of magnitude, comprises said planes within the solid.
  • a tetrahedron is constructed by structural elements, each element with discrete locations, "regular" locations, at equal, linear increments for the length of the structural element. 2. At each vertex, each included angle is 60 degrees, or a multiple thereof
  • each vertex is the apex of a miniature tetrahedron, with each side the uniform length of one increment.
  • Each miniature tetrahedron, or subcomponent of the solid is regularly displaced by angular increments of 60 degrees, in a uniform, angular relationship to every other subcomponent in the solid of the tetrahedron.
  • Each subcomponent therefore can move the dimensional information in its structure to the position of any other subcomponent in the solid, and nevertheless be in identical linear and angular relationship to every, corresponding subcomponent in the entire tetrahedron solid.
  • This invention provides "irregular" points for every point in the solid of that subcomponent.
  • Each irregular point is connected by one or more connectors, or linear distances, positioning that irregular point in relation to one or more locations at equal increments in the solid of that subcomponent.
  • every point in the solid is at least an "irregular" point as described. Therefore every irregular point in its subcomponent can be moved to any other subcomponent in the entire tetrahedron solid, and remain in identical linear and angular relationship to every corresponding location in the entire tetrahedron. There is no dimensional warping, even of irregular locations. Therefore, even two irregular locations in the same or different subcomponents, remain in the same dimensional relationship to every, corresponding .irregular point in the entire solid. CONCLUSION: THEREFORE THIS INVENTION IS FREE OF DIMENSIONAL WARPING.
  • Transmission gate "the output is a function of the inputs... "the logic gate”. (M-H, p. 97) switches “if a particular combination of input signals exists”. (M-H, p. 98, switching gate).
  • a vector is a "directed line segment. As such, vectors have magnitude and direction.” (M-H, p. 358) Therefore a vector can position an "Irregular" point in the solid of a tetrahedron, if its angle is not in a 60 degree, angular relationship to the lines which construct its associated tetrahedron,
  • the length of time required by this computer can be one microsecond. Therefore this computer can make decisions at the rate of one new decision each microsecond. Each decision can be based upon preset criteria represented by vectors 1, 2, and 3 in Fig.1a
  • each vector In a respective microsecond, the electrical characteristics of each vector can be decide the best way to serve an underprivileged person, as evaluated by the criteria present in relation to each vector.
  • the electrical characteristics can he connected to a "transmission gate", a “logic gate” at apex U of Fig. 1b.
  • the logic gate actuates plane V, plane VI, or plane I, 1n accordance with "the particular combination of input signals" in the respective microsecond for the respective beneficiary.

Abstract

In the tetrahedron solid (32), the angular and linear relationships among regular and irregular points (O, V, N, U, X, Y, W) are predetermined, and measured by electrical impulses. The predetermined linear and angular relationships between and among any plurality of random, irregular points (O, V, N, U, X, Y, W) in a tetrahedron solid (32), are arrayed in a common relationships to a mosaic of regular locations (O, V, N, U, X, W) in the tetrahedron solid. The linear and angular relationships are represented by corresponding measurements. The tetrahedron solid (32) is a computer for the solution of problems, such as complex, simultaneous, linear equations. Variables are represented by corresponding electrical devices such as gates and switches. A complex mathematical problem is present logically in the tetrahedron solid (32). The logical resulsts are measured in the constant, unwarped mosaic of regular points (O, V, N, U, X, Y, W) in the solid of the tetrahedron.

Description

A COMPUTER WITH AN ELECTRONIC MOSAIC OF POINTS IN THE SOLID
OF A TETRAHEDRON
A PROBLEM IS A GEOMETRIC FIGURE
1. "How the Current Method Works"
"Mathematicians visualize such problems as complex geometric solids with millions or billions of facets. Each corner of each facet represents a possible solution. The task of the algorithm is to find the best solution, say the corner at the top, without having to calculate the location of every one." (New York Times. Nov. 1,9, 1984, p. A19)
2. Simplex method ''The simplex method, devised by the mathematician George B. Dantzig in 1947, in affect runs along the edges of the solid, checking one corner after another but always heading in the direction of the best solution." (Ibid.)
3. The Karmarkar algorithm
"The Karmarkar algorithm, by contrast, takes a giant short cut, plunging through the middle of the solid. After selecting an arbitrary Interior point, the algorithm warps the entire structure—in essence, reshaping the problem—in a way designed to bring the chosen point exactly into the center. The next step is to find a new point in the direction of the best solution and to warp the structure again, bringing the new point into the center.
"The repeated transformations, bajed on a technique known as projective geometry, lead rapidly to the best answer."
(Ibid.)
In mathematical problem-solving, the best, known solution at any Instant of time can be described as a "hypothetical solution", and as a hypothesis.
Recent methods in the prior art represent that hypothetical solution as a solid such as a sphere, for example, with the hypothetical solution at the center of the sphere. However, th e distortion of a sphere by "warping the sphere with the best known solution at the center, randomly distorts every other reference point in the sphere. The prior art describes this as "warping" the sphere".
Although the hypothetical solution frequently represents progress, all other reference points in the sphere are displaced by said "warping," in relation to the center of the sphere. The random warping is the result of the error which remains in the best known solution. The "warping" randomly displaces every point in the solid, a sphere, in relation to every other point in the sphere, because the approximate solution is made the center of the sphere. The warping method introduces errors in each successive "solution" to the problem. Because every other point in the solid of the sphere has been randomly displaced in relation to the center of the solid, a sphere. The long felt need The need, therefore, is a method for use of a suitable solid, in a method which accurately represents an unlimited number of individual, relevant values or numbers, completely accurately in relation to every other "point" or "irregular bit of information" in the solid.
This invention describes the tetrahedron ara unique solid among the regular polygons, for many reasons includinn the following. Tetrahedron Structure (A Solid),
Fig, 1a shows four planes assembled into a three-dimensional solid, tetrahedron 32.
Fig, 1-a shows first plane MNO in a horizontal view. Its details not shown here were shown in Fig, 1-e, Plane MNO comprises seventh, eighth, and ninth girders 7, 8, and 9, and star I,
In Fig, 1-a, three additional planes are shown identical to said plane MN, said four planes comp rising a large triangle, plane MSP.
The second plane, NSV, comprises first girder 27, second girder 28, and third girder 26, enclosing star y, Third plane CVP comprises first girder 31, second girder 29, and third girder 30, enclosing star VI, Said first, second, and third planes enclose fourth plane NVO, comprising first girder 7', second girder 8', and third girder 9', enclosing star I'.
Fig, 1-b shows a horizontal view of the structure shown in Fig, 1-a, with planes MNO, NSV, and OVP connected to construct a tetrahedron with its base comprising plane NVO, and with its apex designated U, Said planes are connected at a sixty degree angle in relation to each adjacent plane, by connectors (not shown)
Therefore, within the three-dimensional solid of tetrahderon 32, any location in the mosaic of triangle ACE in its base, is intersected by a line exactly perpendicular to the corresponding location in the mosaic of parallel plane WXY. Similarly, each equilateral plane within the mosaic of plane NVO comprising the base of tetrahedron 32, selectively may be constructed in a parallel plane connected to the corresponding locations of tetrahedron 32, In each mosaic thus constructed, it is apparent that each location is intersected by a Hne exactly perpendicular to the corresponding location in base NVO, within the solid comprising tetrahedron 32.
Similarly, in the construction of tetrahedron 32, first plane MNO, second plane NSV, and third plane OVP comprise the surfaces of tetrahedron 32 shown in Fig. 1-b, Said three planes are identical to base NVO, Therefore any structural element connected to any said mosaic within the solid comprising tetrahedron 32, similarly may be connected to the corresponding locations within the irosalc comprising each of the said surfaces of tetrahedron 32. It is apparent that tetrahedron 32 may be expanded to any order of magnitude, to comprise similar planes within its solid, and similar planes comprising its respective surfaces, with each respective mosaic of said Dlanes and surfaces characterized by the same features as tetrahedron 32, supra,
Similarly, each surface of tetrahedron 32 is identical to its base NVO, Therefore tetrahedron 32 selectively may be rotated to establish any surface as its base, with its respective planes within said solid, and respective surfaces, characterized by the same features as tetrahedron 32, supra,
Therefore-any plurality of tetrahedrons with common surfaces are characterized by the same features as tetrahedron 32, supra.
It is apparent that said features depend uoon the equilateral triangle, in each plane, in each solid, and in its respective mosaic, whereby each included angle comprises 60 degrees, or multiples thereof.
Therefore tetrahedron 32, expanded to any order of magnitude, comprises said planes within the solid.
1. Mosaic of regular locations in a tetrahedron.
A tetrahedron is constructed by structural elements, each element with discrete locations, "regular" locations, at equal, linear increments for the length of the structural element. 2. At each vertex, each included angle is 60 degrees, or a multiple thereof
3. Therefore each vertex is the apex of a miniature tetrahedron, with each side the uniform length of one increment.
4. Each miniature tetrahedron, or subcomponent of the solid, is regularly displaced by angular increments of 60 degrees, in a uniform, angular relationship to every other subcomponent in the solid of the tetrahedron.
5. Each subcomponent therefore can move the dimensional information in its structure to the position of any other subcomponent in the solid, and nevertheless be in identical linear and angular relationship to every, corresponding subcomponent in the entire tetrahedron solid.
6. Therefore the dimensional information in each subcomponent never is "warped" in relation to the solid. Therefore warping will never cause an error in a subsequent computation using said dimensional information.
7. "Irregular" points in a subcomponent.
This invention provides "irregular" points for every point in the solid of that subcomponent. Each irregular point is connected by one or more connectors, or linear distances, positioning that irregular point in relation to one or more locations at equal increments in the solid of that subcomponent.
8. No "warping" even of irregular locations!
Therefore every point in the solid is at least an "irregular" point as described. Therefore every irregular point in its subcomponent can be moved to any other subcomponent in the entire tetrahedron solid, and remain in identical linear and angular relationship to every corresponding location in the entire tetrahedron. There is no dimensional warping, even of irregular locations. Therefore, even two irregular locations in the same or different subcomponents, remain in the same dimensional relationship to every, corresponding .irregular point in the entire solid. CONCLUSION: THEREFORE THIS INVENTION IS FREE OF DIMENSIONAL WARPING.
Computer Technologies
Analog computer. "Uses inputs that are proportional to the Instantaneous value of variablefjuantities." (McGraw-Hill Encyclopedia of Science & Technology, 5th Edition, 1982, hereafter "M-H", p. 488)
Digital computer. "Uses symbolic representations of its variables". (M-H, p. 489) Computer Applications
Computer-aided design and manufacturing "totally integrated CAD/CAM system". (M-H, pp. 490-491)
Numerical Control "The limits of accuracy on a workpiece are now controlled entirely by NC machines". (M-H, p. 491)
Computer Graphics. "Pictorial communication between men and computers". (M-H, p. 492) Graphical Input. "Noninteractive and interactive". (M-H, p. 493) Graphical Output, "plotting time is 30 ysec per point." (M-H, p. 494)
Computer storage technology (M-H, p. 496)
Main memory. "RAM chip densities of 256K bits or more"
(M-H, p. 497 to 499) Microcomputers. (M-H, 499-500 )
Memory Gap Technologies, "access time 1 microsecond - 30 Miniseconds","capacity 107-109bits." (M-H, p. 500) Switching
Transmission gate, "the output is a function of the inputs... "the logic gate". (M-H, p. 97) switches "if a particular combination of input signals exists". (M-H, p. 98, switching gate).
A vector
A vector is a "directed line segment. As such, vectors have magnitude and direction." (M-H, p. 358) Therefore a vector can position an "Irregular" point in the solid of a tetrahedron, if its angle is not in a 60 degree, angular relationship to the lines which construct its associated tetrahedron,
Programming the computer in this invention, in Fig.1a
The length of time required by this computer can be one microsecond. Therefore this computer can make decisions at the rate of one new decision each microsecond. Each decision can be based upon preset criteria represented by vectors 1, 2, and 3 in Fig.1a
In a respective microsecond, the electrical characteristics of each vector can be decide the best way to serve an underprivileged person, as evaluated by the criteria present in relation to each vector.
The electrical characteristics can he connected to a "transmission gate", a "logic gate" at apex U of Fig. 1b. The logic gate actuates plane V, plane VI, or plane I, 1n accordance with "the particular combination of input signals" in the respective microsecond for the respective beneficiary.
Each of the computer technologies described in this application, and other comparable electronic technologies, can be used in any combination in the computer of this invention.

Claims

CLAIM
Whereupon the applicant claims: 1. An improved computer for analyzing information represented by electrical signals, wherein the improvement comprises: A. A mosaic of locations in at least a segment of a tetrahedron,
B. said tetrahedron constructed with structural elements including linear locations at equal increments,
C. at least one electrical signal representing its respectiveportion of said information, D. preset electrical means to respond to said signal by its respective, predetermined response to said respective signal, E. said preset electrical means associated with the mosaic of locations in said tetrahedron.
PCT/US1986/001805 1985-09-03 1986-09-03 A computer with an electronic mosaic of points in the solid of a tetrahedron WO1987001478A1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU63729/86A AU6372986A (en) 1985-09-03 1986-09-03 A computer with an electronic mosaic of points in the solid of a tetrahedron

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
USPCT/US85/1670 1985-09-03
PCT/US1985/001670 WO1987001408A1 (en) 1979-01-08 1985-09-03 A universal construction devices for models, stagecraft, models of matrices and the like

Publications (1)

Publication Number Publication Date
WO1987001478A1 true WO1987001478A1 (en) 1987-03-12

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WO (1) WO1987001478A1 (en)

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR1332044A (en) * 1963-12-16
US3685221A (en) * 1969-10-03 1972-08-22 Joseph J Mangan Expandable platform with building structures thereon
US3978452A (en) * 1974-02-28 1976-08-31 Burroughs Corporation System and method for concurrent and pipeline processing employing a data driven network
US4311906A (en) * 1979-06-27 1982-01-19 Thomson-Csf Mosaic of radiation detectors read by a semiconductor device and a picture pickup system comprising a mosaic of this type
US4384273A (en) * 1981-03-20 1983-05-17 Bell Telephone Laboratories, Incorporated Time warp signal recognition processor for matching signal patterns
US4533993A (en) * 1981-08-18 1985-08-06 National Research Development Corp. Multiple processing cell digital data processor

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR1332044A (en) * 1963-12-16
US3685221A (en) * 1969-10-03 1972-08-22 Joseph J Mangan Expandable platform with building structures thereon
US3978452A (en) * 1974-02-28 1976-08-31 Burroughs Corporation System and method for concurrent and pipeline processing employing a data driven network
US4311906A (en) * 1979-06-27 1982-01-19 Thomson-Csf Mosaic of radiation detectors read by a semiconductor device and a picture pickup system comprising a mosaic of this type
US4384273A (en) * 1981-03-20 1983-05-17 Bell Telephone Laboratories, Incorporated Time warp signal recognition processor for matching signal patterns
US4533993A (en) * 1981-08-18 1985-08-06 National Research Development Corp. Multiple processing cell digital data processor

Also Published As

Publication number Publication date
EP0233866A1 (en) 1987-09-02
EP0236436A1 (en) 1987-09-16

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