Знание без граници Le Trou Noir



страница1/6
Дата13.09.2016
Размер0.54 Mb.
  1   2   3   4   5   6
Знание без граници

Le Trou Noir

The Black Hole

Черната дупка


Jean-Pierre Petit

Jean-Pierre Petit

Жан-Пиер Пети
Traduit par :

Translated by :

Превод : Елена Ст. Владова (Elena Vladova)

_____________________________________________________________________

1

Si cet Univers est le meilleur des univers possibles, que sont donc les autres ?



_____________________________________________________________________

If this universe is the best of all possible worlds, I’m glad I don’t live in any of the others.

_____________________________________________________________________
Ако Вселената е съвършеният свят, какви са тогава останалите?

_____________________________________________________________________

2
_____________________________________________________________________

3

Monsieur Albert ! Qu'est-ce que vous faites ?


_____________________________________________________________________

MR. Albert ! What are you doing ?


_____________________________________________________________________

Господин Албер, какво правите?


__________________________________________________________________

Tiens, Anselme, assieds-toi

_____________________________________________________________________

Haf’ a seat, Archibald.

_____________________________________________________________________

Чакай, Анселм. Седни.


_____________________________________________________________________

C'est quoi ?

_____________________________________________________________________

What’s this ?

_____________________________________________________________________
Какво е това?

_____________________________________________________________

Le Cosmol, Anselme, le Cosmol ......

.... qui ouvre la Porte

_____________________________________________________________________

Cosmol, Archibald : der Cosmol ...

Dat points der way.
_____________________________________________________________________
Космол, Анселм. Космол... Той отваря Вратата.

________________________________________________________________________

La Porte, quelle Porte ?

Je ne comprends pas

_____________________________________________________________________

The way ? What way ?

I don’t understand.

_____________________________________________________________________


Вратата? Каква врата? Не разбирам.
________________________________________________________________________

Comprendre ! Ah oui ...

... comprendre ...

_____________________________________________________________________

Understand ? Oh, Ja, unnerstan’ ...

_____________________________________________________________________


Да разбереш? О, да...

... да разбереш...

_____________________________________________________________________

Les autres disent : démarche logique

... c'est de la foutaise !

_____________________________________________________________________

Everyone says you haf’ to think logically ... dat’s garbage !

_____________________________________________________________________


Хората го наричат логическо мислене.

... това са глупости. _____________________________________________________________________

Seul ... le Cosmol ...

.. ouvre la Porte ..

_____________________________________________________________________

Only ... Cosmol ...

can point der way ...
_____________________________________________________________________

Само Космолът може да отвори Вратата.


_______________________________________________________________

... Foutaise ...

_____________________________________________________________________

... Garbage ...


_____________________________________________________________________

Дрън-дрън...


La Porte, oui la Porte ...

_____________________________________________________________________

The way ? Oh, that way ! way out ...
_____________________________________________________________________

Вратата, да Вратата...


__________________________________________________________

4

Du Grand Univers



_____________________________________________________________________

..........

_____________________________________________________________________
На Голямата Вселена.

_____________________________________________________________________

... Univers ...

_____________________________________________________________________

..........

_____________________________________________________________________

Вселена...
___________________________________________________________________

... Univers ...

_____________________________________________________________________

..........

_____________________________________________________________________
Вселена...

Cosmol


Космол

_______________________________________________________

Monsieur Albert !

_____________________________________________________________________

MR. Albert ?
_____________________________________________________________________

Господин Албер!


_________________________________________

Sophie !


_____________________________________________________________________

Sophie ?


_____________________________________________________________________

Софи!
___________________________________________________

Hum ...

_____________________________________________________________________



Hum ...

Х-м...


_____________________________________________________________________

Encore ces nuées ...

_____________________________________________________________________

These cloups again ...

_____________________________________________________________________

Пак има облаци...

__________________________________________________________

........
_____________________________________________________________________

5

Once more, Archie sets out to explore The world of Mists.



_____________________________________________________________________

Une fois de plus, Anselme part explorer des mondes nébuleux.

Анселм отново се кани да изследва мъгляви светове...
Tiens, qu'est-ce que c'est que ce truc là ? On dirait un rouleau pour court de tennis,

ou une sorte de rouleau à peinture.

_____________________________________________________________________

Gosh, what’s this gadget ? It looks like a roller for a tennis court ... or maybe for

painting things.
_____________________________________________________________________

Я виж, какво е това? Прилича на валяк за тенис корт или пък за боядисване.


_____________________________________________________________________

On peut le déplacer TOUT DROIT, sans effort.

Par contre, impossible de dévier d'un poil à DROITE ou à GAUCHE.

_____________________________________________________________________

I can push it STRAIGHT AHEAD without any trouble. But it won’t budge a hair’s

breadth to RIGHT or LEFT.

_____________________________________________________________________
Мога лесно да го преместя НАПРЕД, но не и ВДЯСНО и ВЛЯВО.

__________________________________________________________

A quoi sert cette poignée ? Tiens, elle supprime l'adhérence et me permet de temps en temps de changer de direction.

_____________________________________________________________________

I wonder what this handle’s for ?

Aha ! It unsticks the roller and lets me change direction every so often.

_____________________________________________________________________

За какво служи тази дръжка? Я виж, тя раздвижва валяка и ми позволява от време на време да сменя посоката.

__________________________________________________________

Grâce à cet appareil, Anselme peut tracer les GÉODÉSIQUES d'une surface.

A l'aide de trois géodésiques, Anselme peut tracer des TRIANGLES :

_____________________________________________________________________

With the aid of this strange device, Archie can draw GEODESICS on a surface.

Using these geodesics, he can draw TRIANGLES :


_____________________________________________________________________
Благодарение на този апарат Анселм може да начертае ГЕОДЕЗИЧЕСКИТЕ ЛИНИИ върху една повърхност. Благодарение на трите геодезически линии Анселм може да начертае ТРИЪГЪЛНИЦИ.

___________________________________________________________________

Une surface est un ESPACE À DEUX DIMENSIONS. C’est-à-dire qu’il faut DEUX

QUANTITÉS pour y repérer la position d’un point, deux coordonnées.

_____________________________________________________________________

A surface is a 2 - DIMENSIONAL SPACE. That is, you need TWO numbers – two

coordinates – to specify the position of a point.
_____________________________________________________________________
Повърхността е ПРОСТРАНСТВО С ДВЕ ИЗМЕРЕНИЯ. Тоест, нужни са ДВЕ ВЕЛИЧНИ, две координати, за да се определи позицията на една точка.

___________________________________________________________________

6

Voyons, quand l'espace est EUCLIDIEN, la somme des angles de mon triangle vaut 180 °.



_____________________________________________________________________

Lesse ... If the space is EUCLIDEAN, then the sum of the angles of a triangle is 180°. *


_____________________________________________________________________

Да видим. Когато пространството е ЕВКЛИДОВО, сумата от ъглите е 180 °.(*) _____________________________________________________________________

Quand l'espace a une courbure négative, cette somme est INFÉRIEURE à 180 degrés

_____________________________________________________________________

When the space has negative curvature, the sum is LESS than 180°.
_____________________________________________________________________

Когато пространството има отрицателна кривина, сборът е ПО-МАЛЪК от 180°.


_____________________________________________________________________

Dans un espace à courbure POSITIVE, la somme est SUPÉRIEURE à 180 degrés


_____________________________________________________________________

In a space of positive curvature, it’s GREATER than 180°.


_____________________________________________________________________
В пространство с ПОЛОЖИТЕЛНА кривина сумата е ПО-ГОЛЯМА от 180°.
_____________________________________________________________________

ESPACES À COURBURE VARIABLE :
_____________________________________________________________________

SPACES WITH VARIABLE CURVATURE
_____________________________________________________________________

ПРОСТРАНСТВА С ПРОМЕНЛИВА КРИВИНА
_____________________________________________________________________

J'ai inventé un curvimètre. Il est constitué de trois lamelles élastiques pouvant tourner

librement autour de trois rivets A, B, C.

_____________________________________________________________________

Here’s the cunning inventor with his new brainchild, the CURVIMETER. It’s made from three flexible strips which can turn freely about three rivets A, B, and C.

_____________________________________________________________________


Изобретих уред за измерване на кривините. Той се състои от три еластични пластини, които могат да се въртят свободно около трите нита A, B и C.
_____________________________________________________________________

Il suffit de le plaquer sur une surface et de mesurer les angles à l'aide des trois rapporteurs

pour connaître la COURBURE LOCALE.

_____________________________________________________________________

To find the LOCAL CURVATURE it suffices to lay the curvimeter on the surface and measure the angles with the built-in protractors.
_____________________________________________________________________
Достатъчно е да се постави върху една повърхност и да се измерят ъглите с помощта на трите ъгломера, за да се изчисли ЛОКАЛНАТА КРИВИНА.
_____________________________________________________________________

COURBURE POSITIVE

_____________________________________________________________________

POSITIVE CURVATURE


_____________________________________________________________________
ПОЗИТИВНА КРИВИНА
_____________________________________________________________________

COURBURE NÉGATIVE

_____________________________________________________________________

NEGATIVE CURVATURE


_____________________________________________________________________

НЕГАТИВНА КРИВИНА
_____________________________________________________________________

(*) Pour plus de détails, voir le GÉOMÉTRICON, du même auteur, Editions BELIN.


_____________________________________________________________________

(*) For further details, see here’s looking at euclid in the same series.


_____________________________________________________________________
(*) За повече подробности, виж ГЕОМЕТРИКОН от същия автор.

_____________________________________________________________________

7

Cette bosse ménagée dans un plan est constituée d’une région centrale à



courbure positive, entourée par une région à courbure négative.

_____________________________________________________________________

This bump in the plane is made from a central region of positive curvature, surrounded

by a region of negative curvature.

_____________________________________________________________________

Тази изпъкналост в равнинаната се състои от централна част с положителна кривина, заобиколена от зона с отрицателна кривина.

_____________________________________________________________________

ZÔNE À COURBURE POSITIVE

ZÔNE À COURBURE NÉGATIVE

ZÔNE À COURBURE NULLE

_____________________________________________________________________

REGION OF POSITIVE CURVATURE

REGION OF NEGATIVE CURVATURE

REGION OF ZERO CURVATURE

_____________________________________________________________________

ЗОНА С ПОЛОЖИТЕЛНА КРИВИНА

ЗОНА С ОТРИЦАТЕЛНА КРИВИНА

ЗОНА С НУЛЕВА КРИВИНА


_____________________________________________________________________

Du point de vue de la COURBURE, le CREUX est identique à la BOSSE

_____________________________________________________________________

From the point of view of curvature, a dent is just like a bump.


_____________________________________________________________________

От гледна точка на КРИВИНАТА ВДЛЪБНАТИНАТА е равна на ИЗПЪКНАЛОСТТА.

_____________________________________________________________________
COURBURE POSITIVE

COURBURE NULLE

COURBURE NÉGATIVE

_____________________________________________________________________

POSITIVE CURVATURE

ZERO CURVATURE

NEGATIVE CURVATURE

_____________________________________________________________________

ПОЛОЖИТЕЛНА КРИВИНА

НУЛЕВА КРИВИНА

ОТРИЦАТЕЛНА КРИВИНА

_____________________________________________________________________

Sauf erreur, ceci est un TORE.

_____________________________________________________________________

Crikey, if I ain’t mistaken, h’it’s a blinkin’ TORUS.

_____________________________________________________________________

Ако не греша, това е геометрична фигура тор.

_____________________________________________________________________

Oui, il y a une bande à courbure positive, une autre à courbure négative, séparées par

une frontière où la courbure est nulle.

_____________________________________________________________________

I’m a VIRGO myself ...

Oh, I see. Yes, there’s a band of positive curvature and a band of negative curvature, separated by a frontier having zero curvature.

_____________________________________________________________________

Да, една зона е с положителна кривина, друга с отрицателна кривина, а двете са разделени от граница с нулева кривина.

_____________________________________________________________________

Cette dernière pouvant être déterminée en mettant le tore en sandwich entre deux plans.
_____________________________________________________________________

To find the frontier, make a TORUSBUGER using two planes for buns.


_____________________________________________________________________

Тази граница може да бъде изчислена и да превърне тора на сандвич между две равнини.


_____________________________________________________________________

Mon cher Tirésias, avez-vous réalisé que votre coquille était un espace bidimensionnel

à courbure variable ?

_____________________________________________________________________

Tiresias, old fruit, ‘as it ever struck yer that shell is just a two-dimensional space wiv

variable curvyture ?

_____________________________________________________________________

Уважаеми Тирезий, забелязахте ли, че вашата черупка е двуизмерно пространство с променлива кривина?


_____________________________________________________________________

mi !..


_____________________________________________________________________

eeep !
_____________________________________________________________________

Ами-и-и...

_____________________________________________________________________

Léon, laisse Tirésias tranquille !
_____________________________________________________________________

Lenny, stop bugging Tiresias !

_____________________________________________________________________

Леон, остави Тирезий на мира!

_____________________________________________________________________

8

POINTS CÔNIQUES

_____________________________________________________________________

CONICAL POINTS
_____________________________________________________________________

ТОЧКИ НА КОНУСА

_____________________________________________________________________

Tu vas voir, Anselme, il y a des choses plus étranges encore.

_____________________________________________________________________

You’ll soon see, Archie, that there are even stranger things.

_____________________________________________________________________

Анселм, ще видиш, че има и още по-странни неща.

_____________________________________________________________________

Dépêche-toi, Tirésias, j’ai soif de connaître ...
_____________________________________________________________________

Buzz off, Tiresias – I sense a thirst for knowledge coming upon me ...


_____________________________________________________________________

Побързай, Тирезий, искам да науча още...

_____________________________________________________________________

Attends-moi !


_____________________________________________________________________

Wait for boo-boo !


_____________________________________________________________________

Чакай ме!


_____________________________________________________________________

Tu vois, Tirésias, je vais MAILLER ma surface en entrecroisant des géodésiques,

ce qui me donnera des tas de triangles

_____________________________________________________________________

Watch, Tiresias – I’m going to draw a grid on the surface by meshing geodesics. That’ll

give me HEAPS of triangles.

_____________________________________________________________________

Виждаш ли, Тирезий, сега ще сплета в МРЕЖА моето пространство и като пресека геодезическите линии, ще получа много триъгълници.

_____________________________________________________________________

Coquille à courbure variable ... Je t’en ficherais, moi !!..

_____________________________________________________________________

Typical – Archie’s meshing about again !


_____________________________________________________________________

Черупка с променлива кривина!

_____________________________________________________________________

Alors là, je n’y comprends plus rien ! Que se passe-t-il autour de ce point P ?


_____________________________________________________________________

Oh lord, I can’t see what’s going on at all ! What’s happening around this point P ?


_____________________________________________________________________

Нищо не разбирам. Какво става около тази точка P ?


_____________________________________________________________________

Tu n’as qu’à utiliser ton curvimètre.


_____________________________________________________________________

The cunning inventor has forgotten to use his curvimeter.


_____________________________________________________________________

Трябва да използваш уреда за измерване на кривини.

_____________________________________________________________________

9

Enfin, Sophie, que se passe-t-il ? Si le triangle du curvimètre ne contient pas ce point P,



il indique une courbure nulle.

_____________________________________________________________________

Hey, Sophie – What’s going on ? If the curvimeter’s triangle doesn’t contain the point P,

it says the curvature is zero.

_____________________________________________________________________

Софи, какво става? Ако триъгълникът на уреда за измерване на кривини не съдържа тази точка Р, той показва нулева кривина.

_____________________________________________________________________

Mais si le point P est dans le triangle, alors c’est courbe !

_____________________________________________________________________

But if P is inside the triangle, then the space is curved !


_____________________________________________________________________

Но точка Р е в самия триъгълник, значи пространството е изкривено.

_____________________________________________________________________

C’est un point cônique. Tiens, regarde, je prends un plan, J’ENLÈVE un secteur

d’angle θ et je recouds.

_____________________________________________________________________

It’s a CONICAL POINT. Look – suppose I take a plane, cut out a sector with angle θ,

and join it up again.

_____________________________________________________________________

Това е ТОЧКА НА КОНУСА. Виж, взимам една плоскост, отрязвам един сектор с ъгъл θ и отново зашивам плоскостта.

_____________________________________________________________________

PLAN
_____________________________________________________________________

PLANE
_____________________________________________________________________

ПЛОСКОСТ


_____________________________________________________________________

J’obtiens un cône que nous appellerons un POSICÔNE

_____________________________________________________________________

I get a kind of cone, which we’ll call a POSICONE


_____________________________________________________________________

Получавам конус, който наричаме ПОЛОЖИТЕЛЕН КОНУС.


_____________________________________________________________________

Vous pouvez vérifier, avec du carton. Un rouleau de papier collant vous aidera à

matérialiser facilement les géodésiques.

_____________________________________________________________________

You can test it out with a piece of cardboard. A roll of sticky tape will help you find

geodesics easily.

_____________________________________________________________________

Можете да направите същото с картон. Ролка тиксо ще ви помогне да намерите геодезическите линии.


_____________________________________________________________________

10

Bon, alors, si mon triangle contient le sommet d’un cône, la somme de ses angles est



toujours supérieure à 180° !

_____________________________________________________________________

Oh, I see ! If my triangle contains the tip of a cone then the sum of the angles is always greater than 180°.

_____________________________________________________________________

Добре. Значи, ако моят триъгълник съдържа върха на конус, сборът от ъглите е винаги по-голям от 180° !

_____________________________________________________________________

Pas si vite ! En entaillant mon plan je vais maintenant au contraire RAJOUTER

un secteur d’angle θ.

_____________________________________________________________________

Hold your horses ! It’s not that simple ! Suppose instead I slit the plane and add a sector

with angle θ.
_____________________________________________________________________

Не бързай. Когато сглобявам моята плоскост, ще направя обратното – ще ДОБАВЯ един сектор с ъгъл θ.


_____________________________________________________________________

Alors ... Ça fera un NÉGACÔNE ?


_____________________________________________________________________

Don’ tell me – yer gets a blinkin’ NEGACONE.


_____________________________________________________________________

Значи, ще се получи ОТРИЦАТЕЛЕН КОНУС.

_____________________________________________________________________

Cette fois-ci, quand le triangle entoure le point P, la somme des angles vaut 180° - θ !


_____________________________________________________________________

This time, if the triangle contains the point P, the angle-sum will be 180°- θ, smaller

than 180°.

_____________________________________________________________________

Този път, когато точка Р е в триъгълника, сумата от ъглите ще бъде 180° - θ ! ___________________________________________________________________

Mais, de nouveau, quand le point est en dehors du triangle, la somme vaut 180°.


_____________________________________________________________________

But if the point is outside the triangle, the sum is 180° again.


_____________________________________________________________________

Но когато точката е извън триъгълника, сумата е отново 180°.

_____________________________________________________________________

Cette propriété des cônes est indépendante de la taille du triangle, que celui-ci soit

minuscule ou gigantesque.
_____________________________________________________________________

This property of cones is independent of the size of the triangle : you get the same result whether it’s large or small.


_____________________________________________________________________

Това свойство на конусите не зависи от размера на триъгълника, дали той е малък или голям.


_____________________________________________________________________

11

Mais ... quand même ! ...



c’est courbe ou c’est pas courbe ?

_____________________________________________________________________

But – That’s crazy !

Is the stupid thing curved, or not ?

_____________________________________________________________________

Но, все пак...

Това кривина ли е или не?

_____________________________________________________________________

Un point cônique, Anselme, c’est de la courbure concentrée

_____________________________________________________________________

A conical point, Archie, is a concentrated piece of curvature.

_____________________________________________________________________

Точката на конуса, Анселм, е концентрична кривина.

_____________________________________________________________________

Entre les points côniques, l’espace est euclidien, sans courbure
_____________________________________________________________________

Away from the conical point, the space is (locally) euclidean, without any curvature.


_____________________________________________________________________

Пространството между точките на конуса е евклидово, без кривина.

_____________________________________________________________________

L’angle θ est la mesure de cette quantité de courbure

_____________________________________________________________________

The angle θ measures the amount of curvature at the conical point.

_____________________________________________________________________

Ъгъл θ е мярката за тази кривина.

_____________________________________________________________________

Ouvre ton cône et mets le à plat

_____________________________________________________________________

Open your cone and lay it out flat.

_____________________________________________________________________

Разтвори твоя конус и го разгъни.

_____________________________________________________________________

POSICÔNE


_____________________________________________________________________

POSICONE


_____________________________________________________________________

ПОЛОЖИТЕЛЕН КОНУС

_____________________________________________________________________

Voici le résultat de l’opération, faite par Anselme, dans le cas d’un cône à courbure

positive.

_____________________________________________________________________

Here’s what Archie got, when he opened out a cone having positive curvature.
_____________________________________________________________________

Ето резултата от операцията, извършена от Анселм, когато конусът е с положителна кривина.

_____________________________________________________________________

Et dans le cas d’un cône à courbure négative


_____________________________________________________________________

Where as, in the case of negative curvature ...


_____________________________________________________________________

И когато конусът е с отрицателна кривина.


_____________________________________________________________________

NÉGACÔNE
_____________________________________________________________________

NEGACONE

_____________________________________________________________________

ОТРИЦАТЕЛЕН КОНУС

_____________________________________________________________________

12

Prenons une surface PLANE et maillons-la avec des géodésiques formant un quadrillage



régulier. On dira qu’on a PAVÉ cette surface avec des carrés, tous identiques. Si nous

suivons une TRAJECTOIRE, un TRAJET, tel qu’on coupe les côtés des carrés successifs

sous un même angle, ce trajet s effectuera selon une géodésique de la surface.

La Direction

_____________________________________________________________________

Take a PLANE surface and rule it with geodesics to from a regular square grid. We say that the surface has been tiled with identical squares. If we follow a path, or TRAJECTORY, that cuts each successive square at the same angle, then this path will always be a geodesic on the surface.

The Boss

_____________________________________________________________________

Да вземем едно РАВНО пространство и да прокараме през него геодезическите линии, за да получим решетка от правилни квадрати. Все едно сме НАЧЕРТАЛИ в пространството еднакви квадрати. Ако прокараме ТРАЕКТОРИЯ така, че да отрежем краищата на последователни квадрати под един и същи ъгъл, то тази траектория ще мине по геодезическата линия на повърхността.

Ръководството

_____________________________________________________________________

Mais, pourquoi ne pas faire cela sur une sphère ?

_____________________________________________________________________

So what stops me from doing the same on a sphere ?

_____________________________________________________________________

Но защо това да не може да се направи и с една сфера?


_____________________________________________________________________

Primo, essaie de PAVER une sphère avec des carrés, bien jointifs, tu m’en diras

des nouvelles.

_____________________________________________________________________

Well, you might start by trying to tile a sphere neatly with squares that would be novel.
_____________________________________________________________________

Ако успееш да НАЧЕРТАЕШ в сферата последователни квадрати, ела да ми кажеш!

_____________________________________________________________________

Les méridiens d’une sphère sont des géodésiques de celle-ci. Un trajet coupant ces

méridiens sous un angle constant, différent de 90°, mènerait invariablement vers l’un des

PÔLES !


_____________________________________________________________________

The meridians of a sphere are its geodesics. A path cutting the meridians at a constant angle, other than 90°, will invariably wind towards one of the POLES !

_____________________________________________________________________

Меридианите на една сфера са геодезическите й линии. Линия, която преминава през тези меридиани под постоянен ъгъл, различен от 90°, ще ни отведе неминуемо до ЕДИН ОТ ПОЛЮСИТЕ.

_____________________________________________________________________

Une navigation à cap constant mène ... au pôle !

_____________________________________________________________________

Navigation on a fixed heading leads to ... the pole !

_____________________________________________________________________

Плаването с постоянен курс води до... полюса.


_____________________________________________________________________

PÔLE
_____________________________________________________________________

POLE
_____________________________________________________________________

ПОЛЮС


_____________________________________________________________________

13

En coupant les méridiens de la sphère à 90°, je me déplacerais suivant des parallèles



_____________________________________________________________________

If I cuts the meriddyuns of a sphere at 90°, I go along one o’ the parallels.

_____________________________________________________________________

Пресичайки меридианите на сферата на 90°, ще се движа по паралелите.

_____________________________________________________________________

parallèles qui ne sont pas de géodésiques. Vu ! (*)


_____________________________________________________________________

But parallels ain’t geo-deesicks. Gottit ! (*)

_____________________________________________________________________

Паралели, които не са геодезически линии ! (*)

____________________________________________________________________

Je peux recouvrir une surface plane, euclidienne, à l’aide d’éléments plans, quadrillés

_____________________________________________________________________

I can get a plane euclidean surface by fitting together a lot of flat grids.

_____________________________________________________________________

Мога отново да получа равно евклидово пространство с помощта на квадратни елементи.

_____________________________________________________________________

Et si je me déplace en coupant ces maillages sous un angle constant, à condition de bien assurer les raccords, de proche en proche, j’obtiendrai une géodésique.


_____________________________________________________________________

And if I move by cutting the grid lines at a fixed angle, remembering to keep everything consistent when I switch grids, then I’ll get a geodesic.

_____________________________________________________________________
А ако се движа, като пресичам тези квадрати под постоянен ъгъл, при условие, че те са добре свързани, малко по малко се доближавам до геодезическата линия.

_____________________________________________________________________

POSICÔNE

_____________________________________________________________________

POSICONE

____________________________________________________________________

ПОЛОЖИТЕЛЕН КОНУС

_____________________________________________________________________

NÉGACÔNE
_____________________________________________________________________

NEGACONE

_____________________________________________________________________

ОТРИЦАТЕЛЕН КОНУС


_____________________________________________________________________

Ce moyen simple donne également les géodésiques du cylindre, qui sont en forme de

ressort à boudin
_____________________________________________________________________

You can do the same thing on a cylinder – just like a salami in a string bag.

_____________________________________________________________________

По този прост начин се получават и геодезическите линии на цилиндъра, които имат формата на спирална пружина.

_____________________________________________________________________

(*) On ne peut les tracer, sur la sphère, à l’aide de ruban adhésif (sauf l’équateur).


_____________________________________________________________________

(*) You can’t draw a parallel on a sphere with sticky tape, except at the equator.

Try it on a basketball.

_____________________________________________________________________

(*) Не можем да очертаем паралелите върху сферата с помощта на тиксо, с изключение на Екватора.

_____________________________________________________________________

14

Voici pourquoi la somme des angles d’un triangle, sur un posicône, s’accroît de l’angle



de découpe θ :

_____________________________________________________________________

Here’s why the angle-sum of a triangle, on a posicone, is increased by the angle θ of

the cut.

_____________________________________________________________________

Ето защо сумата от ъглите на един триъгълник на позитивен конус се увеличава от ъгъла на рязане θ.

_____________________________________________________________________

Anselme va maintenant construire des cônes particuliers, dans lesquels la régularité du maillage peut être conservée

La Direction

_____________________________________________________________________

Archibald higgins will now construct special cones, which keep the tiling regular.

The Boss

_____________________________________________________________________

Сега Анселм ще направи отделни конуси, с правилно разграфяване.

Ръководството

_____________________________________________________________________

Là, j’enlève 90°.

_____________________________________________________________________

There, I’ve cut out 90°.

_____________________________________________________________________

Ето, отрязвам под 90°.

_____________________________________________________________________

Sur un tel cône, tu peux tracer des triangles rectangles équilatéraux.
_____________________________________________________________________

On this cone you can draw right-angled equilateral triangles.


_____________________________________________________________________

Върху този конус можеш да нарисуваш правоъгълни равностранни триъгълници.


_____________________________________________________________________

15

Maintenant, j’enlève un secteur de 180°.


_____________________________________________________________________

Now I excise a sector of 180°.

_____________________________________________________________________

Сега ще отрежа сектор под 180°.

_____________________________________________________________________

Sur un tel cône, la somme des angles d’un triangle vaut 360°


_____________________________________________________________________

On this cone, yer gits a h’angle – sum of 360°.


_____________________________________________________________________

Върху такъв конус сумата от ъглите на един триъгълник ще е равна на 360°.


_____________________________________________________________________

Ce qui signifie que l’on pourrait tracer dessus, à l’aide de ses géodésiques, un triangle

ayant trois angles égaux à 120°, donc obtus.
_____________________________________________________________________

Which implies that you can draw on it, using geodesics, a triangle having three angles

of 120° - that is, OBTUSE.

_____________________________________________________________________

Което означава, че отгоре може да се начертае с помощта на геодезическите линии триъгълик с три ъгъла по 120°, тоест ТЪПИ.

_____________________________________________________________________

Et il se refermerait quand même ?

_____________________________________________________________________

And it still closes up ? That’s weird.

_____________________________________________________________________

Дори и ако се затвори?

_____________________________________________________________________

Hum ...

____________________________________________________________________



Hum ...

_____________________________________________________________________

Х-м...

_____________________________________________________________________



Bien sûr, mon cher Tirésias, c’est vous qui êtes obtus !

_____________________________________________________________________

Seems ter me, Tiresias, that YOU’RE the one wot’s h’obtuse !

_____________________________________________________________________

Разбира се, уважаеми Тирезий, вие сте тъп!

_____________________________________________________________________

mi !
_____________________________________________________________________

Me ?
_____________________________________________________________________

Аз?

_____________________________________________________________________



16

Sur ce cône, on peut tracer des BIANGLES, la somme des angles valant 180°.

_____________________________________________________________________

On this cone you can draw BIANGLES. The angle-sum is 180°.

_____________________________________________________________________

Върху този конус могат да се начертаят ДВУЪГЪЛНИЦИ, сумата от чиито ъгли ще е равна на 180°.

_____________________________________________________________________

Attendez ! là, je ne comprends plus ...

On parlait des triangles. Voilà maintenant des BIANGLES. Pourquoi pas, la prochaine

fois, des .... monoangles ?!?!....


_____________________________________________________________________

'Old it ! Nar yer lorst me ...

First it wuz triangles. Nar it’s blinkin’ biangles. Wozzit gonna be next ? monoangles ?
_____________________________________________________________________

Чакайте! Вече нищо не разбирам! Ставаше въпрос за триъгълници. Сега пък за ДВУЪГЪЛНИЦИ. А другия път за едноъгълници ли ще говорим?


_____________________________________________________________________

LE CÔNE VU DE DESSUS


_____________________________________________________________________

The cone viewed from above


_____________________________________________________________________

ИЗГЛЕД КЪМ КОНУСА ОТГОРЕ


_____________________________________________________________________

Tous ces objets sont des POLYGONES


_____________________________________________________________________

It’s OK ; They’re all POLYGONS.


_____________________________________________________________________

Всички те са с МНОГО КОНУСИ.

_____________________________________________________________________

DANS LE PLAN :

La somme des angles d’un

- triangle vaut 180°

- quadrangle vaut 180° + 180° = 360°

- pentangle vaut 180° + 180° + 180° = 540°

_____________________________________________________________________

In the PLANE :

The angle-sum of a

- triangle is 180°

- quadrilateral is 180° + 180° = 360°

- pentagon is 180° + 180° + 180° = 540°

_____________________________________________________________________

На ПОВЪРХНИНАТА:

Сумата от ъглита на един:

- триъгълник е равна на 180°

- четириъгълник е равна на 180° + 180° = 360°

- петоъгълник е равна на 180° + 180° + 180° = 540°


Etc

И т. н.


_____________________________________________________________________

Je craque ...

_____________________________________________________________________

I’m goin’ bonkers ...

_____________________________________________________________________

Ще се побъркам...

_____________________________________________________________________

Et dans le cas du BIANGLE, réduit à un segment, cette somme est nulle


_____________________________________________________________________

And for a BIANGLE, which reduces to a line segment, the sum is zero.


_____________________________________________________________________

В случая с ДВУЪГЪЛНИКА, сведен до линия, сумата е нула.


_____________________________________________________________________

17

Pourquoi 180° de plus à chaque fois que l’on rajoute un sommet ?


_____________________________________________________________________

Why the h’extra 180° every time yer adds a corner ?


_____________________________________________________________________

Защо сумата се увеличава със 180° всеки път, когато добавим някой ъгъл?


_____________________________________________________________________

Hop !


_____________________________________________________________________

Ha !


_____________________________________________________________________

Хоп!


_____________________________________________________________________

Ceci devrait vous éclairer

_____________________________________________________________________

A simple KARATE CHOP will make it clear ...

_____________________________________________________________________

Сега трябва да ви просветне...


_____________________________________________________________________

Bon, continuons ...


_____________________________________________________________________

All right, you two, let’s get on with it.


_____________________________________________________________________

Да продължим...

_____________________________________________________________________

Je vais maintenant enlever les trois quarts du plan.


_____________________________________________________________________

Now I cut out three quaters of the plane.


_____________________________________________________________________

Сега ще отрежа три четвърти от плоскостта.


_____________________________________________________________________

On dirait une serviette de table


_____________________________________________________________________

You might call that a NAPKONE


_____________________________________________________________________

Прилича на салфетка.

_____________________________________________________________________

Et quand je la regarde par le bout


_____________________________________________________________________

And when I look at the end ...


_____________________________________________________________________

И когато гледам през нея от единия край...


_____________________________________________________________________

Anselme obtient ceci


_____________________________________________________________________

Archie sees this


_____________________________________________________________________

Ето какво вижда Анселм.


_____________________________________________________________________

18

Sur ce cône, toutes les géodésiques se recoupent elles mêmes (elles se recoupent ici à



angle droit). On peut donc y tracer des monoangles
_____________________________________________________________________

On such a cone, every geodesic will intersect itself (here at a right angle), so you can

draw MONOANGLES.
_____________________________________________________________________

Върху този конус всички геодезически линии съвпадат (съвпадат под прав ъгъл). Значи можем да начертаем едноъгълници.

_____________________________________________________________________

C’était donc vrai !


_____________________________________________________________________

Crikey ! I thought I was jokin’ !


_____________________________________________________________________

Значи съм бил прав.

_____________________________________________________________________

Tout dépend de l’angle θ du cône


_____________________________________________________________________

It all depends on the angle θ of the cone.


_____________________________________________________________________

Всичко зависи от ъгъла θ на конуса.


_____________________________________________________________________

Les géodésiques ne se referment pas


_____________________________________________________________________

Geodesics don’t close up.


_____________________________________________________________________

Геодезическите линии не се затварят.

_____________________________________________________________________

cas limite


_____________________________________________________________________

Limiting case.


_____________________________________________________________________

Краен случай.


_____________________________________________________________________

Les géodésiques se referment


_____________________________________________________________________

Geodesics close up.


_____________________________________________________________________

Геодезическите линии се затварят.


_____________________________________________________________________
  1   2   3   4   5   6


База данных защищена авторским правом ©obuch.info 2016
отнасят до администрацията

    Начална страница