Abstract:
An exhibit to assist in teaching mathematical properties to individuals may include a tricycle with square wheels. The tricycle may be mounted on a circular track with arcuate segments that effectively smooth out the motion imparted by the square wheels.

Description:
FIELD OF THE DISCLOSURE 
     The present disclosure relates to a tricycle used to demonstrate mathematical properties and particularly to a square wheeled tricycle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  illustrates the motion of a square wheel. 
         FIG. 1B  illustrates the motion of a center point of the square wheel of  FIG. 1A . 
         FIG. 2  illustrates the motion of a center point of a square wheel wherein the center point stays at a predetermined level. 
         FIGS. 3A &amp; 3B  illustrate a top and side view respectively of a track suitable for use with a square wheel tricycle of the present disclosure. 
         FIG. 4  illustrates an interior side view of an exemplary square wheel tricycle of the present disclosure. 
         FIG. 5  illustrates a rear view of the square wheel tricycle of  FIG. 4 . 
         FIG. 6  illustrates a top view of the square wheel tricycle of  FIG. 4 . 
         FIG. 7  illustrates a close up view of an exemplary gear mechanism for the square wheel tricycle of  FIG. 4 . 
         FIG. 8  illustrates the tricycle of  FIG. 4  on the track of  FIG. 3 . 
         FIG. 9  illustrates a resilient member on a square wheel to cushion rotation of the square wheel. 
     
    
    
     DETAILED DESCRIPTION 
     Mathematics is often underappreciated for its ubiquity, beauty, and capacity to entertain, especially amongst children. By demonstrating mathematics in an entertaining manner, a greater understanding and a greater appreciation of the field may occur. The present disclosure provides a system suitable for use as an exhibit that demonstrates mathematical properties of objects in motion and particularly demonstrates the unlikely situation where an individual may ride a tricycle with square wheels relatively smoothly without the expected bumps and lurches as the square wheels rotate. The exhibit shows that mathematics can be applied to many fields, including recreation. It creates an association between mathematics and fun. It also shows how mathematics connects many fields, because the shape of the arches in the base is a catenary curve, which is the same shape (but upside down) of a length of chain when held at two locations. Furthermore, it illustrates how the circumference grows linearly with radius, because the wheels which are further from the center of the base need to be proportionally larger. Before addressing the particulars of the system, a brief overview of square wheel motion is provided with reference to  FIGS. 1A and 1B . 
     In general, if a square wheel  10  is rotated along a straight surface  11  in a direction  12 , the corners  10 A,  10 B,  10 C, and  10 D sequentially strike the surface  11  as is well understood. The center point  10 E traces out a periodic arcuate path  13  as illustrated in  FIG. 1B . If an interested party were to try to ride a bicycle or tricycle with square wheels, the arcuate movement of the center point  10 E would be conveyed through the frame of the bike to the rider, making a bumpy ride. 
     In contrast, if the square wheel  10  is placed on a path  14  having arcuate humps  16  and troughs  18 , the arcuate motion of the center point  10 E may be smoothed out, especially if the arcuate length of the humps  16  corresponds to the length of a side of the square  10 . That is, the path  14  may be designed such that the length of the side of the wheel  10  between corners  10 A and  10 B equals the length  16 C (the distance between points  16 A and  16 B or successive troughs  18 ). In exemplary embodiment, the humps  16  have a catenary shape. A catenary shape is the curve assumed by a cord of uniform density and cross section that is perfectly flexible but not capable of being stretched that hangs freely from two fixed points. A catenary shape hump  16  allows for exact compensation of a square wheel assuming that the length of the side of the wheel corresponds to the arcuate length of the hump  16 . 
       FIGS. 3A &amp; 3B  illustrate an endless track  20  for use with a square wheel tricycle. In particular, the track  20  is a circular disc and has radially extending bumps  22  and troughs  24  corresponding to the humps  16  of  FIG. 2 . The center portion  26  may be flat (illustrated), have a decorative motif, or continue the bumps  22  and troughs  24  as desired (not illustrated). Visual indicia  28  and  30  may be painted or otherwise created on the surface of the track  20  to guide a rider on the track, and in an exemplary embodiment is a solid or dotted line painted on the disc. In particular, indicia  28  may be aligned with a central or front wheel of the tricycle and indicia  30  may be for the rear wheels of the tricycle, where indicia  30 A corresponds to an outer or exterior back wheel and indicia  30 B corresponds to an inner or interior back wheel. In an exemplary embodiment, the endless track  20  is sixteen feet (4.88 m) in diameter and divided into thirty-two identical segments (bumps  22 ). In this exemplary embodiment, the center portion  26  may be four feet (1.22 m) in diameter. 
     The tricycle  40  is illustrated in  FIGS. 4-6 .  FIG. 4  illustrates a left side view of the tricycle  40 . The tricycle  40  has a frame  42 , a seat  44 , handles  46  and fork  48 , which holds front square wheel  50  in place. Front wheel  50  is rigidly affixed to pedals  52  on either side of the front wheel  50  as is common in tricycles. When motive force is applied to the pedals  52 , the front wheel  50  turns and motion is imparted to the tricycle  40 . The tricycle  40  further has rear square wheels  54  and  56 . Rear wheel  54  is an exterior wheel and is larger than interior rear wheel  56 . The sizing differential is dictated by the nature of the endless track  20 . Specifically, indicia  30 A, on which exterior rear wheel  54  will rest and follow has a greater diameter, and thus a larger circumference than indicia  30 B, on which interior rear wheel  56  will rest and follow. Thus, when the tricycle navigates around the endless track  20 , exterior rear wheel  54  must be larger to cover the same radial sweep of movement. Rear wheels  54  and  56  are connected to one another by a gear box  58  (illustrated in  FIGS. 5-7 ). 
     As better illustrated in  FIG. 6 , frame  42  and fork  48  are angled so that the tricycle  40  will be forced to turn as it is driven forward when motive force is applied to the pedals  52 . In an exemplary embodiment, the angle of the frame  42  and the front wheel  50  are coupled to the size of the wheels and the radius of the indicia  30  on the endless track  20  so as to allow the tricycle  40  to move around the endless track  20  on the indicia  30  without requiring the operator to steer. That is, the handles  46  are locked into a fixed position, and the operator may rest her hands on the handles, but the operator is not able to change the rate of turning or the direction of travel. 
     In an exemplary embodiment, the overall length of the tricycle  40  is based on a span of 33.75 degrees at the radius traveled by the front wheel  50 . This may be shortened or lengthened as desired. The angle between the frame  42  and the rear axle is the shortest distance between the center of the rear axle and center of the steering neck. This angle evenly divides the deflection from perpendicular at the joint between the rear axle and the frame  42 , and the angle at the front wheel  50  orients the path of the front wheel  50  perpendicular to the radius of its travel. The orientation of the frame  42  places the rider&#39;s weight toward the center of the travel path, which nicely offsets the tendency of tricycles to become unstable in a direction opposite to the direction of turning. In an exemplary embodiment, the frame height is approximately 18-26 inches, depending on whether sized for a child or an adult. Variations on the frame height are within the scope of the present disclosure. 
     By way of example, an exemplary adult sized tricycle  40  may have a twenty-four inch (60.96 cm) offset between rear wheels  54 ,  56 . An exemplary child sized tricycle  40  may have a twenty inch (50.8 cm) offset between rear wheels  54 ,  56 . This offset provides reasonable stability for the tricycle  40 . Likewise, in an exemplary embodiment to maintain stability, the height of the saddle (seat  44 ) should not greatly exceed the offset between the rear wheels. 
     An exemplary gear box  58  is better illustrated in  FIG. 7  and is designed to keep rear wheels  54  and  56  in a fixed relative position to one another (e.g., rotating at the same rate). To effectuate this, exterior rear wheel  54  is rigidly affixed to first shaft  60  and interior rear wheel  56  is rigidly affixed to second shaft  62 . Shafts  60  and  62  pass through respective apertures (not illustrated) in gear frame  64  and freely rotate within the respective apertures. First shaft  60  has first gear  66  and second shaft  62  has second gear  68 , which interoperate through third gear  70 . Thus, as rear wheels  54  and  56  rotate (because someone is using the pedals  52  to drive the front wheel  50  and the front wheel  50  is turning, thereby pulling the tricycle  40  forward, causing the rear wheels to rotate), the shafts  60  and  62  rotate, which in turn causes the gears  66  and  68  to rotate. The gears  66  and  68  are kept in step with one another by the third gear  70 . Forcing the wheels to rotate at the same rate helps keep the tricycle  40  at a given radius on the endless track  20 . While this attribute of concurrently rotation makes for a smoother ride, other gear boxes may be used to achieve the same result. 
       FIG. 8  illustrates and overhead shot of a person  72  riding the tricycle  40  on the endless track  20 . As is illustrated, the front wheel  50  follows the visual indicia  28  and rear wheels follow indicia  30 A and  30 B. Given the angle of the frame  42  and the angle at which the front wheel  50  is fixed relative to the frame  42 , when the person  72  pushes the pedals  52 , the tricycle  40  moves around in a circle staying at a fixed radius from the center of the endless track  20 . In this manner, the person  72  may continue to pedal around the circle until they grow tired of the activity. Spectators may view the motion of the square wheels and see how the square wheels interact with the bumps  22  and troughs  24  of the endless track  20 . In this manner, mathematical properties are exhibited in an interactive and enjoyable fashion. 
     In an exemplary embodiment, visual indicia  28 ,  30  may be duplicated so that two tricycles  40  may operate on the endless track  20  concurrently. With a sixteen foot diameter endless track  20 , it is possible to lay the visual indicia  28 ,  30  on the endless track in such a manner that adequate clearance between the wheels and pedals of the two tricycles is provided (e.g. approximately ten to twelve inches clearance). Likewise, such an arrangement may still provide a respectable distance (e.g., six-twelve inches) between the exterior rear wheel  54  of the larger outer tricycle and the outer edge of the endless track  20  as well as between the interior wheel  56  of the smaller inner tricycle and the center portion  25 . 
     In an exemplary embodiment, assuming two tricycles  40  riding on the endless track  20 , the wheel sizes may be as follows: 20.0494 inch per side for the exterior rear wheel  54  on the outer tricycle (operating at a 90 inch radius); 17.3761 inch per side for the front wheel  50  of the outer tricycle (operating at a 78 inch radius); 14.7029 inch per side for the interior rear wheel  56  of the outer tricycle (operating at a 66 inch radius); and 12.0296 inch per side for the exterior rear wheel  54  for the inner tricycle (operating at a 54 inch radius); 9.8019 inch per side for the front wheel  50  of the inner tricycle (operating at a 44 inch radius); and 7.5742 inch per side for the interior rear wheel  56  of the inner tricycle (operating at a 34 inch radius). The wheel sizes are dictated by the radius at which the wheels operate and conform to the following equation (given  32  bumps  22 ):
 
Side of wheel  S =(2 *π*r )/(32*arcsin  h   (1))
 
     Note that if the tricycles  40  are moved to operate at different radii or with different clearances between tricycles and/or the edges of the endless track  20 , the size of the wheels will change accordingly, and such adjustments are within the scope of the present disclosure. Likewise, if the size of the endless track  20 , or number of bumps  22  changes, the size of the wheels will change. Such variations are within the scope of the present disclosure. 
       FIG. 9  illustrates an exemplary square wheel  80 , which may serve as front wheel  50  or rear wheels  54 ,  56 . The wheel  80  is square and substantially rigid. It may be made from a solid planar material including, but not limited to metal, wood or plastic. Alternatively, the square wheel  80  may include spokes (not illustrated) as is well understood. The outer edges of the wheel  80  are cushioned by a resilient member  82 , divided into long flat portions  84  and corner portions  86 , and made from a material such as rubber (natural or synthetic) or foam, and which may be secured to the wheel through an adhesive or a fastener. Corner portions  86  may be thicker than long flat portions  84  to allow for the greater wear and tear that the corners experience while in use. Likewise, by making the corner portions  86  effectively modular relative to the rest of the resilient member  82 , the corner portions  86  may be replaced with ease as the corner portions exhibit wear. In an exemplary embodiment, the wheels  80  are ¾ inch (1.91 cm) thick and made from a material such as HDPE. With this thickness there is approximately a ⅙ inch difference in the side length of the squares, so the squares may be beveled to function smoothly. Alternatively, the resilient member  82  may mitigate the need for such beveling. 
     In an alternate embodiment, not illustrated, a motor may be applied to the gear box along with a power switch and/or a throttle and the tricycle may be propelled around the track by operation of the motor rather than manual force being applied to the pedals. The motor may be electric and have an associated battery or it may be a combustion engine operating on hydrogen or a fossil fuel or the like. Instead of a manually operated power switch and throttle, there may be a computer controlled system in place, including one where the onboard computer wirelessly communicates to a remote computer and the remote computer provides instructions on the operation of the tricycle in much the same manner that a radio controlled toy car may operate. Such a computer operated system may have a control system embodied in the computer processing unit, a display and appropriate input and output devices such as a display and appropriate wireless transmission capability. The programs that operate such a computer may be stored on an appropriate computer readable medium. 
     In an alternate embodiment, more than one set of indicia may be placed on the endless track  20  and tricycles with appropriately sized wheels may ride on the different indicia. Indicia having a smaller radius may support a smaller tricycle, allowing small children to experience the exhibit, while indicia having a larger radius may support larger tricycles, allowing adults to experience the exhibit. In a variation on this embodiment, the tricycles may travel in different directions (clockwise and counterclockwise) around the endless track  20  as desired. 
     While it is contemplated that the frames of the tricycles may be made from steel, other materials may also be used such as titanium, aluminum, or the like. 
     In an alternate embodiment, signage may be present near the system which explains the math behind the system as well as any particular applications or instructions which may be imparted to an audience. 
     In an alternate embodiment, the number of wheels on the tricycle  40  may be varied. Two and four wheel permutations are readily within the scope of the present disclosure. Thus, as used herein the term bicycle includes tricycles and quad-bikes and the term tricycle includes cart or four-wheeled (quad-wheeled) bike. Such a cart is also termed a quad-bike herein. 
     RULES OF INTERPRETATION &amp; GENERAL DEFINITIONS 
     Numerous embodiments are described in this disclosure, and are presented for illustrative purposes only. The described embodiments are not, and are not intended to be, limiting in any sense. The presently disclosed invention(s) are widely applicable to numerous embodiments, as is readily apparent from the disclosure. One of ordinary skill in the art will recognize that the disclosed invention(s) may be practiced with various modifications and alterations, such as structural, logical, software, and electrical modifications. Although particular features of the disclosed invention(s) may be described with reference to one or more particular embodiments and/or drawings, it should be understood that such features are not limited to usage in the one or more particular embodiments or drawings with reference to which they are described, unless expressly specified otherwise. 
     The present disclosure is neither a literal description of all embodiments nor a listing of features of the invention that must be present in all embodiments. 
     Neither the Title (set forth at the beginning of the first page of this disclosure) nor the Abstract (set forth at the end of this disclosure) is to be taken as limiting in any way as the scope of the disclosed invention(s). 
     The term “product” means any machine, manufacture and/or composition of matter as contemplated by 35 U.S.C. §101, unless expressly specified otherwise. 
     The terms “an embodiment”, “embodiment”, “embodiments”, “the embodiment”, “the embodiments”, “one or more embodiments”, “some embodiments”, “one embodiment” and the like mean “one or more (but not all) disclosed embodiments”, unless expressly specified otherwise. 
     The terms “the invention” and “the present invention” and the like mean “one or more embodiments of the present invention.” 
     A reference to “another embodiment” in describing an embodiment does not imply that the referenced embodiment is mutually exclusive with another embodiment (e.g., an embodiment described before the referenced embodiment), unless expressly specified otherwise. 
     The terms “including”, “comprising” and variations thereof mean “including but not limited to”, unless expressly specified otherwise. 
     The terms “a”, “an” and “the” mean “one or more”, unless expressly specified otherwise. 
     The term “plurality” means “two or more”, unless expressly specified otherwise. 
     The term “herein” means “in the present disclosure, including anything which may be incorporated by reference”, unless expressly specified otherwise. 
     The phrase “at least one of”, when such phrase modifies a plurality of things (such as an enumerated list of things) means any combination of one or more of those things, unless expressly specified otherwise. For example, the phrase at least one of a widget, a car and a wheel means either (i) a widget, (ii) a car, (iii) a wheel, (iv) a widget and a car, (v) a widget and a wheel, (vi) a car and a wheel, or (vii) a widget, a car and a wheel. 
     The phrase “based on” does not mean “based only on”, unless expressly specified otherwise. In other words, the phrase “based on” describes both “based only on” and “based at least on”. 
     Where a limitation of a first claim would cover one of a feature as well as more than one of a feature (e.g., a limitation such as “at least one widget” covers one widget as well as more than one widget), and where in a second claim that depends on the first claim, the second claim uses a definite article “the” to refer to the limitation (e.g., “the widget”), this does not imply that the first claim covers only one of the feature, and this does not imply that the second claim covers only one of the feature (e.g., “the widget” can cover both one widget and more than one widget). 
     Each process (whether called a method, algorithm or otherwise) inherently includes one or more steps, and therefore all references to a “step” or “steps” of a process have an inherent antecedent basis in the mere recitation of the term ‘process’ or a like term. Accordingly, any reference in a claim to a ‘step’ or ‘steps’ of a process has sufficient antecedent basis. 
     When an ordinal number (such as “first”, “second”, “third” and so on) is used as an adjective before a term, that ordinal number is used (unless expressly specified otherwise) merely to indicate a particular feature, such as to distinguish that particular feature from another feature that is described by the same term or by a similar term. For example, a “first widget” may be so named merely to distinguish it from, e.g., a “second widget”. Thus, the mere usage of the ordinal numbers “first” and “second” before the term “widget” does not indicate any other relationship between the two widgets, and likewise does not indicate any other characteristics of either or both widgets. For example, the mere usage of the ordinal numbers “first” and “second” before the term “widget” (1) does not indicate that either widget comes before or after any other in order or location; (2) does not indicate that either widget occurs or acts before or after any other in time; and (3) does not indicate that either widget ranks above or below any other, as in importance or quality. In addition, the mere usage of ordinal numbers does not define a numerical limit to the features identified with the ordinal numbers. For example, the mere usage of the ordinal numbers “first” and “second” before the term “widget” does not indicate that there must be no more than two widgets. 
     When a single device or article is described herein, more than one device or article (whether or not they cooperate) may alternatively be used in place of the single device or article that is described. Accordingly, the functionality that is described as being possessed by a device may alternatively be possessed by more than one device or article (whether or not they cooperate). 
     Similarly, where more than one device or article is described herein (whether or not they cooperate), a single device or article may alternatively be used in place of the more than one device or article that is described. For example, a plurality of computer-based devices may be substituted with a single computer-based device. Accordingly, the various functionality that is described as being possessed by more than one device or article may alternatively be possessed by a single device or article. 
     The functionality and/or the features of a single device that is described may be alternatively embodied by one or more other devices that are described but are not explicitly described as having such functionality and/or features. Thus, other embodiments need not include the described device itself, but rather can include the one or more other devices which would, in those other embodiments, have such functionality/features. 
     Devices that are in communication with each other need not be in continuous communication with each other, unless expressly specified otherwise. On the contrary, such devices need only transmit to each other as necessary or desirable, and may actually refrain from exchanging data most of the time. For example, a machine in communication with another machine may not transmit data to the other machine for weeks at a time. In addition, devices that are in communication with each other may communicate directly or indirectly through one or more intermediaries. 
     A description of an embodiment with several components or features does not imply that all or even any of such components and/or features are required. On the contrary, a variety of optional components are described to illustrate the wide variety of possible embodiments of the present disclosure. Unless otherwise specified explicitly, no component and/or feature is essential or required. 
     Further, although process steps, algorithms or the like may be described in a sequential order, such processes may be configured to work in different orders. In other words, any sequence or order of steps that may be explicitly described does not necessarily indicate a requirement that the steps be performed in that order. The steps of processes described herein may be performed in any order practical. Further, some steps may be performed simultaneously despite being described or implied as occurring non-simultaneously (e.g., because one step is described after the other step). Moreover, the illustration of a process by its depiction in a drawing does not imply that the illustrated process is exclusive of other variations and modifications thereto, does not imply that the illustrated process or any of its steps are necessary to the invention, and does not imply that the illustrated process is preferred. 
     Although a process may be described as including a plurality of steps, that does not indicate that all or even any of the steps are essential or required. Various other embodiments within the scope of the described invention(s) include other processes that omit some or all of the described steps. Unless otherwise specified explicitly, no step is essential or required. 
     Although a product may be described as including a plurality of components, aspects, qualities, characteristics and/or features, that does not indicate that all of the plurality are essential or required. Various other embodiments within the scope of the described invention(s) include other products that omit some or all of the described plurality. 
     An enumerated list of items (which may or may not be numbered) does not imply that any or all of the items are mutually exclusive, unless expressly specified otherwise. Likewise, an enumerated list of items (which may or may not be numbered) does not imply that any or all of the items are comprehensive of any category, unless expressly specified otherwise. For example, the enumerated list “a computer, a laptop, a PDA” does not imply that any or all of the three items of that list are mutually exclusive and does not imply that any or all of the three items of that list are comprehensive of any category. 
     Headings of sections provided in this disclosure are for convenience only, and are not to be taken as limiting the disclosure in any way. 
     “Determining” something can be performed in a variety of manners and therefore the term “determining” (and like terms) includes calculating, computing, deriving, looking up (e.g., in a table, database or data structure), ascertaining, recognizing, and the like. 
     A “display” as that term is used herein is an area that conveys information to a viewer. The information may be dynamic, in which case, an LCD, LED, CRT, LDP, rear projection, front projection, or the like may be used to form the display. The aspect ratio of the display may be 4:3, 16:9, or the like. Furthermore, the resolution of the display may be any appropriate resolution such as 480i, 480p, 720p, 1080i, 1080p or the like. The format of information sent to the display may be any appropriate format such as standard definition (SDTV), enhanced definition (EDTV), high definition (HD), or the like. The information may likewise be static, in which case, painted glass may be used to form the display. Note that static information may be presented on a display capable of displaying dynamic information if desired. 
     The present disclosure refers to a “control system”. A control system, as that term is used herein, may be a computer processor coupled with an operating system, device drivers, and appropriate programs (collectively “software”) with instructions to provide the functionality described for the control system. The software is stored in an associated memory device (sometimes referred to as a computer readable medium). While it is contemplated that an appropriately programmed general purpose computer or computing device may be used, it is also contemplated that hard-wired circuitry or custom hardware (e.g., an application specific integrated circuit (ASIC)) may be used in place of, or in combination with, software instructions for implementation of the processes of various embodiments. Thus, embodiments are not limited to any specific combination of hardware and software. 
     A “processor” means any one or more microprocessors, CPU devices, computing devices, microcontrollers, digital signal processors, or like devices. Exemplary processors are the INTEL PENTIUM or AMD ATHLON processors. 
     The term “computer-readable medium” refers to any medium that participates in providing data (e.g., instructions) that may be read by a computer, a processor or a like device. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks and other persistent memory. Volatile media include DRAM, which typically constitutes the main memory. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise a system bus coupled to the processor. Transmission media may include or convey acoustic waves, light waves and electromagnetic emissions, such as those generated during RF and IR data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM, a FLASH-EEPROM, a USB memory stick, a dongle, any other memory chip or cartridge, a carrier wave, or any other medium from which a computer can read. 
     Various forms of computer readable media may be involved in carrying sequences of instructions to a processor. For example, sequences of instruction (i) may be delivered from RAM to a processor, (ii) may be carried over a wireless transmission medium, and/or (iii) may be formatted according to numerous formats, standards or protocols. For a more exhaustive list of protocols, the term “network” is defined below and includes many exemplary protocols that are also applicable here. 
     It will be readily apparent that the various methods and algorithms described herein may be implemented by a control system and/or the instructions of the software may be designed to carry out the processes of the present disclosure. 
     As used herein a “network” is an environment wherein one or more computing devices may communicate with one another. Such devices may communicate directly or indirectly, via a wired or wireless medium such as the Internet, Local Area Network (LAN), Wide Area Network (WAN), or Ethernet (or IEEE 802.3), Token Ring, or via any appropriate communications means or combination of communications means. Exemplary protocols include but are not limited to: BLUETOOTH™, TDMA, CDMA, GSM, EDGE, GPRS, WCDMA, AMPS, D-AMPS, IEEE 802.11 (WI-FI), IEEE 802.3, TCP/IP, or the like. Note that if video signals or large files are being sent over the network, a broadband network may be used to alleviate delays associated with the transfer of such large files, however, such is not strictly required. Each of the devices is adapted to communicate on such a communication means. Any number and type of machines may be in communication via the network. Where the network is the Internet, communications over the Internet may be through a website maintained by a computer on a remote server or over an online data network including commercial online service providers, bulletin board systems, and the like. In yet other embodiments, the devices may communicate with one another over RF, cellular networks, cable TV, satellite links, and the like. Where appropriate encryption or other security measures such as logins and passwords may be provided to protect proprietary or confidential information. 
     Communication among computers and devices may be encrypted to insure privacy and prevent fraud in any of a variety of ways well known in the art. Appropriate cryptographic protocols for bolstering system security are described in Schneier, APPLIED CRYPTOGRAPHY, PROTOCOLS, ALGORITHMS, AND SOURCE CODE IN C, John Wiley &amp; Sons, Inc. 2d ed., 1996, which is incorporated by reference in its entirety.