CA1140175A - Multicolored globe adapted to make combinations between colors on multitudinous directions - Google Patents

Abstract

MULTI COLORED GLOBE ADAPTED TO MAKE COMBINATIONS
BETWEEN COLORES ON MULTITUDINOUS DIRECTIONS
ABSTRACT
This invention relates to a globe divided by an equatorial line and by a plurality of symmetrical meridional lines in a plurality of spherical triangles which are grouped on different colores between two poles. Every couple of symmetrical meridians divides the globe in two hemispheres which can be turned so that one hemisphere change the poles, and also the equator divides the globe in other two hemi-spheres which can rotate independently. Combining this plurality of spacial rotations disposed on different angles between them, becomes possible to make arrangements of spherical triangles and to get different symmetrical colored designs according to everyone ability.

Description

S~'~ARY OF THE INVENTION
The present invention has been devised with the general object of providing apparatus by means of which colored spherical triangles shaping a globe can be arranged in definite orders turning on many angles. The apherical triangles have a great mobility, but in the meantime they are partially interdependently moving always in groups, a group being formed by half of them. Making globes with different number of spherical triangles, and for the same number of spherical triangles on a globe, varying the number of chosen colores, it is possible to obtain various globes from the simplest to the most complex, and consequently the same will be the problems to be solved.

- 1 of 10 -A main object of the present invention is to provide an apparatus, by which people can spend their leisure til~e a~reeably anA usefully solving the globe's problems, and further~ore improving the observation, memory, computation and ingenuity.
A ~Irther object of the present invention is to prov de di~ferent globes concernin~ thcir complexity, suitable for children, youth or adults, ~nd for any grade of discernment.
A further object of the present invention is to satisf~ people by finding at their level the key of problems without great effort, and choosing grad~lally the n-ext level of difficulty.
The invention is described in detail in the following;, ~vith reference to the accompanying dra~ings and schemes sho~ving the embodiments of an apparatus and the ~vay of solvin~ cer-tain of globe's problems.

BRI~F ]~F,SCRIPTION ~F T}l~ ~'.A~ GS ~n S~,HEMES
FIG. 1 is a side elevation of a globe according to the invention.
,?~ FIG. ? i s a top plan view of t}~e globe.
FIG. 3 is a sectional view along line 3-3 in FIG. 1.
FIG. 4 is a sectional view alon~ line 4-4 in FIG. 1~
FIG. 5 is a sectional view ~long line 5-5 in FIG. 1.
FIG. 6 is a sectional vi e~'! along line 6-6 in FIG. 2.
FIG. ~ is a top nlan view of internal framework.
FIG. 8 is a vie~v c~ ong llne 8-8 in ~IG. 7.
FIG. 9 is an enlarged, cross-sectional view of a ~ole.

FIG. 10 is ~n enlargeA, top plc~n view of a pole.
FIG. 11 is an enlarged, urlderneath view of a pole.
?~ FIG. 1~ is ~n enlarged top ~lan vie~/ of the globe without pole.

_ ? ~!f ]0 3~'75 FIG. 13 shows schematically four globes wi-th different spherical triangles and col.r.~rs.
FIG. 1l~ shows schematically e,ar(lples of symmetrical designs of a globe ~.vith 1~ triangles and two colors.
~ IG. 15 shows schematically examples of symmetrical designs of a globe with 16 triangles and -four colors.
~ 'IG. 16 shows schematical.ly ex~n~les of symmetrical designs of a globe with 32 tri.angles and four colors.
FIG. 17 sho~s schematically the key of an exercise 1 n from FIG. ]4.
FIG. 1~ shows schel~ati.cally the lcey of an exercise from FIG. 15.
FIG. 1~ shows scherlatically the ]cey of another exercise from FIG. 15~

~ETAI _D DESÇRIPTI~!N F AN l~ ,ODI~iT~.~'IT ~ T~IE
INVENTlCN AND ',~.~'P~ES 0~ ITS UTI~ITY
The apparatus il].ustrated is a globe FIG. 1 and FIG. 2 comoosed of 16 spherical triangles 1 joined together between two poles 2. Spherical triangles 1 have their sides

2~ marled by equatorial line 3 and by meridional lines 4.
A spherical triangle 1 has a shell ~ bounded by gliding means 8 on meridionc~l lines ~ cm d a thiclcened part 26 on equatorial li.ne 3. Spherical tri.angles 1 are set together by spheric~l channe~s 9 which are disposed inside the globe and which have gl.iding means 10 in slidable engagement with gliding means 8. Both gli.ding means 8 and 10 are hoo]c shaped for preventlng the detachment of spherical triangles 1 but allowing a sliding movemen-t betweren -them. The long axis 11 FIG. 3 of spherical channel 9 is a con.:r.~ntric circle with local. meridian 17 of adjacent spherical trianglres 1, and r) ~

- li4~5 the ex-tentions of sides 7 cro.,s each other upon a circle (not sho~) concentric2.1].y ~.ri.-th the same loca] meridian 12, ~nd edges 2~ of ~liding rne~ns ~, an(l 10 arc contained in -planes (not sho~n) ~hich are l?a.ra].lel ~!ith the ~lane of local meridian 12. G].iding mef~ls ~ and channels 9 are long from equatorial line to a ci.rcl.e pl.aced toward the pole ~here s~hericc~. channels 9 join togethfr side by side as in ~IG. 5.
S~herlcal triangles 1 are grouped by sphericc~llchannels 9 i.n t~vo he~ispheres, th~ top hemisphere 13 and the lo~ hemi-ln snhere 1l~. These t~o hemispheres are held together by poles 2fixed to an internc~l frarne~orl~ FIG. 6 ~hich includes axle 15 and enuatorial d;sk ]6. T.~en hemisphere 13 rotates over hemi-s~here lL~ s~herical channels 9 slide over thiclrened parts 26 of sphericc~l trian~les 1. The encls of thic~;ened parts 26 are sli~htly sloped close to e~uatori~ line 3 (not shotvn) for an easy rotation Or s,nherical chc~nne]s 9 Over thicl;ened parts 26. Each end of axle ].5 is a~ia]ly cut in half shaping spindle ]7 for loclsing pole 2. Close to spindle 17, axle 15 includes two partic~l disl~s 18 tYhich have gliding means 19 Partial dislss 18 restrain from rotation half of splleric~l tri.angles 1 an(l half plus t~o Or snheric~l channels 9 about the local meridic?n 20 FI~T. 6 p~.sing through the dic~meter of sninclle 17, ~nd gllding m~s 19 establish the continuity of gliding me.~ns 10 for gliding means 8 of spherical tri.angles 1 placed in the vicinity of par-ti~l dis'.s 18 an;l freed for rotation about ].ocal meridi~n 20 l~IG. 6. The encls of gliding mcans 8 are sli.~rhtly sloped (not sho~..rn) ~or en~agill~ easily in rotation ~ith g].id;ng means ].0 and 19. E~uatorial disl~ 16 is surroundcd by arc 21 T,~hich ensure a correct axial position

3~ î or hemi.spheres 13 and 1l~. Pole 2 includes semicircuiar clentation 7? matching ~!Jith s~indle ]7, ancl rib 27 for handl.ing ~ Il of ]~ _ 114~17S

from outside axle 15. ~ach pole 2 is fi.xed to a le 15 by means of scre~r 28 ~rhich interloc!cs sp;nrlle 17 -through hole 25, Shells ~ of spherical triangles 1 a-re cut toward poles 2 shaping ho]es 6 for alloNing the rota-tion of spindle 17.
The globe as described is divi~ed in two hemi-spheres 13 and 1ll by the e~uatorial line 3 and in 8 hemi-sphères by the rnerldional lines l,, ~here are 5 planes of rotation, one equatorial and four meridional planes.
Hemis~heres 13 and lll are free for independently rotation n bet~veen them and each one has its spherical triangles 1 and spherical channels 9 joined together by gliding means 8 and 10. ~he other hemispheres devided by meridionc~l lines 4 are grou~ed in couples by partic~l dis!;s ]8 ~vhich are solid connected ~vith axle 15 and poles 2, Turning pol.es 2 with ribs 27 upon a meridional ]ine 4, a plane of rotation will be established on that meridian and the opposite hemisphere will be independently rotatable. The hemlsphere which rotates on a meridlonal line changes the spherical channels 9 at the plane of rotation because partial disks 18 restrain from ?O rotation the o~posite hemisphere including its adjacent spherical channels 9. Hevlng sph~r;.cal trian~les 1 grouped on different co].ors, and turning them spatial~y as sho~n, any kind of combination bet~veen colors can be obtained so as ~,vill be described furthermore.
FIG. 13 sho.lJs schematically from A'-A" to D'-D"
four differen-t globes. The ]etters A', B', ~' and D' mark the top hemispheres, and the letters A", B", ~`" and D" marlc the 10W hemispheres u~lth their spherical triangles. '~he letters R, Y, B and G represent respectively the col.ors 3~ red9 yellow, blue and green. Imagining the lo;v hemispheres to be transparent, in these schemes -the upper spherical ~ ~ of ~ ~

` 114V~75 triangles of top hemispheres correspond to the upper spherical triangles of 10W hemispheres. FIG. 13 A', A~
shows a globe ~/ith 16 spherical triangles c~nd two colors, red and yellow. FIG. 13 B', B" shows a globe with 16 spherical triangles and four colores, red yellov blue and green. FIG . 13 C', C " shows a globe with 24 spherical triangles and four colores, red, yellow, blue and green.
FIG. 13 D', D" shows a globe with 32 spherical triangles and four colores, red, yellow, blue and green. The mçridional lines being always disposed symmetrically across poles 2, the spherical triangles on each hemisphere (13 and 14) are in pairs and as a result, spherical triangles 1 are always multiples of four. Such combinations are, of course, merely illustrative of the present invention and may be readily modified and equivalents in colors or number to be made by -those skilled in this art.
FIG. 1~ shows schematically from A' - A~ to J'- J~
examples of symmetrical combinations between colores for the globe of FIG. 13 A', An, and FIGS. 1~ and 16 show ~he same thing for the globes of FIG. 13 B', B" and FIG. 13 D', D"
respectively. FIGS. 17, 18 and 19 show different exercises and for that purpose the following symbols have been useds a strong meridionc~l line marks the plane of rotation for two adjacent hemispheres and an arrow beside a strong meridional line marks the hemisphere which rotates changing its poles , a strong circles marks that the equatorial plc~ne is the plane of rotation and an arrow with a digit placed beside circle mar~s the hemisphere which rotates, the direction and the steps of rotation, one step being a spherical triangle. The rotation are n~mbered consecutively by figures 1, 2, 3 etc.

placed between the top hemispheres and the lov hemispheres, - 6 of 10 -FIG. ]7 shows sn exercise for the globe of ~IG. 14, and the eiht rotations to be made for passing from A', A"
to G', G". FIG. lP! shows an exercise for the globe of FIG. 1~ and the eight rotations to be made for passing from A', A" to ~ n, ~IG. 19 shows another exercise for the globe of FIG. 1~ and the nine rotations to be made for passing from A', A" to E', E".
To find the number of all kind of arrangements for different spherical triangles according to their color is necessary to use the theory of permutations. There are t~No main categories of arrangements, the first is a sym-metrical category and the second is at random or nonsym-metrical category. Both categories are important, the first being the category which is to be ordinarily used and the second being the category of great degree of difficulty.
For the globe of FIG. 14, if N denotes the number of permutations of 16 things taken 16 at a time l!sith 2 times things alike, then:

N = -21(68P186) = ~ )= 26.107 The number of s~mmetrical arran~ements is n-10 and may be more than 10 but close to 10.
If M denotes the number of paths from N nonsymmetrical arrangements to those 10 symmetrical arrangements, thens M = 26.107.10 = 26.108 If m denotes the number of paths from a symmetrical arrangement to another symmetrical arrangement and taking in consideration that for one way there is a forward path and a backward path which are distingushed from one another, then: m _ 2.10P2 = 90 It is known from e~ercise of FIG. 17 that the number of rotations between two symmetrical positions are eight, and ~ 7 of 10 for other paths are less than ei&ht or close to eight.
As a consequence ~e observe that inside the s~rmmetrical category is easy enough to pass from one to another arrangement and in the meantime ve observe that from nonsymmetrical category to an arrangement of symrnetrical category is a labyrinth. If turning the hemispheres from one to another symmetrical arrangement we move away from symmetrical category entering in nonsyr~metrical category by a great number of rotations which ~e cannot remember for turning back, we are lost and we can reach the syrnmetrical category only knov~ing and using a series of rules for grouping spherical triangles by colors. If ~e do not kno~l these rules, we can reach the symmetrical c2tegory disconnecting the poles and separating the spherical triangles for forming again the globe in a symmetrical arr2ngament.
These remarks are strengthened by the other globes.
As ex2mple, for the globe of FIG. 15 N = 4 (4lp4l = ~ = 2.10 n = 10 M = 2~1011.10 = 2~1012 m = 2.10P2 = 90 And for the globe of FIG. 16 N ~ 43(28~82) = ~ - 16.1029 n = 10 M = 16.1029.10 = 16.103 m - 2.10P2 _ 90 The multicolored globes shown above can be succes-sfully used by children, teenagers or adults because these globes c2n be manufactured with different grades of difficulty ~nd they never remain lost in the labyrint of nons~nmetrical arrangements being ~ossible to arrange them again symmetrically - ~ of 10

Claims (3)

Having fully described an operative embodiment of this invention and how to be used, I now claims:

1. Apparatus for combining symmetrically different colors on a globe comprising:
a plurality of spherical triangles having their sides marked by a plurality of symmetrical meridional lines and by an equatorial line, each said spherical triangle having a shell bounded by two meridional sides and by en equatorial side and having also a vertex formed by said meridional sides, each said meridional side having first gliding means extending from said equatorial side toward said vertex, said first gliding means being stopped before said vertex so as to have between the ends of said first gliding means an interval equal to the thickness of two said first gliding means put together, and said equatorial side having a thickened part;
a plurality of spherical channels for coupling said spherical triangles between them and having the same length as said first gliding means, each said spherical channel having two second gliding means disposed longitudinally and in slidably engagement with said first gliding means, said first gliding means and said second gliding means being hook shaped for preventing the detachment of said spherical triangles;
two poles placed to either point where said spherical channels converge between them, each said pole being button shaped and having an inside face and an outside face, said inside face having a semicircular dentation placed concentric with said pole and said outside face having a rib placed parallel with the diameter of said semicircular dentation, and said pole having also a hole between said inside face and said outside face for passing a screw through the middle of said semicircular dentation; and - 9 of 10 -a rotatable internal framework inside said globe having an axle perpendicularly solid connected to an equatorial disk, said axle having at each end a semicircular spindle matching with said semicircular dentation of said poles and serving for coupling and fixing said poles to said axle by means of said semicircular spindle and of said screw which turns inside threads made in the middle of said semi -circular spindle, in the vicinity of each end of said axle being perpendicularly placed a partial disk for restraining from rotation a first half of said spherical triangles forming a first hemisphere in comparison with a second half of said spherical triangles forming a second hemisphere, said partial disk having a third gliding means forming a continuity of said second gliding means and for supporting said first gliding means engaged in rotation, said shells being cut toward said poles shaping a hole for allowing the rotation of said first and second hemispheres around said spindle, and said equatorial disk having peripherically an are for maintaining the form of said globe in the vicinity of said equatorial line.

2. Apparatus according to claim 1 wherein: the plurality of said spherical triangles are grouped in sets of different colors.

3. Apparatus according to claim 1 wherein said plurality of spherical triangles are grouped in a plurality of hemispherical couples, said hemispherical couples having their hemispherical components independently rotatable, a first couple being composed of two hemispheres divided between them by said equatorial line end the rest of couples being composed of hemispheres divided between them by said symmetrical lines, said meridional lines being arranged by pairs and said spherical triangles being multiples of four.

- 10 of 10 -