Note: Descriptions are shown in the official language in which they were submitted.
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.
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175
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 -
175
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
175
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
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