Pro milovníky bludišt a geocachingu jsme pripravili dalsi mystery cache do serie a po predcházející verzi 3D musí logicky nasledovat verze 4D.
Ctvrty rozmer nebo ctyrrozmerny prostor (4D) je abstraktni pojem, vznikly zobecnenim pravidel trirozmerneho prostoru. Matematici i filosofove jej studuji uz skoro dve ste let, protoze je zajimavy sam o sobe a nabizi zajimave nahledy na matematiku a pribuzne obory.
Algebraicky vznika tak, ze se pravidla vektoru a souradnicove geometrie uplatni na prostor o ctyrech rozmerech. Ctyrrozmerny vektor (usporadanou ctverici cisel) lze chapat jako umisteni ve ctyrrozmernem prostoru. To je euklidovsky prostor, ktery ma metriku i normu, takze se vsemi rozmery lze zachazet stejne: pridany rozmer se nijak nelisi od ostatnich tri.
Toto a mnohem vic se muzete o 4D docist na Wikipedii a na temze miste muzete spatrit i rotujici teserakt.
V geometrii je teserakt ctyrrozmernou analogii krychle, jde tedy o specialni variantu nadkrychle pro d=4. Vice odborne by mohla byt hyperkrychle definovana jako pravidelny konvexni ctyrúhelnik s osmi krychlovymi nadstenami. Tolik prilis nesouvisejici informace o 4D.
I kdyz jsme se na Wikipedii lehce inspirovali, myslenku na labyrint ci bludište ve 4D jsme rychle opustili a rozhodli se vytvorit neco skromnejsiho. Tak prisel na svet tento labyrint s privlastkem pouze ctvrty v poradi. Presto se vsak od všech predchazejicich lisi.
Jak na cache? Staci v bludisti najit spravnou cestu z mista A do mista B a cestou sesbirat vsechna cisla. Pri trose predstavivosti se da cesta najít pomerne snadno i v 2D.
Soucet vsech sebraných cisel vam da cislo XXX, druhe sebrane cislo je cislo A, predposledni sebrane cislo je cislo B.
Cache pak najdete na: N 50° 03.(XXX+7*A) E 014° 31.(XXX-3*B-A+11)
Kes je sice "small" a kus tuzky v ni najdete, presto doporucujeme nejaké písátko s sebou.
Nahled pro tisk/Picture Preview
For fans of mazes and geocaching we made next mystery cache and the 4D version must logically succeed to the 3D version.
In mathematics, the fourth dimension, or a four-dimensional ("4D") space, is an abstract concept derived by generalizing the rules of three-dimensional space. It has been studied by mathematicians and philosophers for almost two hundred years, both for its own interest and for the insights it offered into mathematics and related fields.
Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.
You can read this and much more about "4D" at Wikipedia and at the same place you can see the rotating tesseract (see above).
In geometry, the tesseract, also called an 8-cell or regular octachoron, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells.
In spite of the inspiration from Wikipedia we threw aside the idea about The Maze #4D and decided to make something more modest. That way this maze came to light with the tag only the fourth.
And what about the cache? You only have to find the right way from the place A to the place B and collect all numbers on your way. If you have a little imagination you can find the way easily even in 2D.
The sum of all collected numbers is number XXX, the second collected number is number A, the next to the last collected number is number B.
Then you can find the cache at: N 50° 03.(XXX+7*A) E 014° 31.(XXX-3*B-A+11)
You will need a pen, so take your own please.
Do serie Labyrintky patri:
Labyrint #1/The Maze #1
Labyrint #2/The Maze #2
Labyrint #3D/The Maze #3D
Labyrint #4/The Maze #4
Labyrint #5/The Maze#5
Labyrint #6/The Maze#6
