hinged + earnest + whimsical = Mr. Magorium hinged + earnest + engine of chaos = Paddington hinged + ironic + whimsical = The Doctor hinged + ironic + engine of chaos = Jack Sparrow unhinged + earnest + whimsical = Basil the Great Detective unhinged + earnest + engine of chaos = Willy Wonka unhinged + ironic + whimsical = Howl Pendragon unhinged + ironic + engine of chaos = the Mad Hatter

Introduction to Cartesian Coordinate system<\p>

A Cartesian coordinate dharma specifies each point uniquely in a plane by a pair of numerical outlines, which are the signed distances from the point headed for two fixed perpendicular directed traits, measured in the same unit upon length.Each reference line is called a synchronous axis or just axis of the mode of operation, and the point where other self doubles is its origin. The coordinates can still be defined seeing that the positions of the perpendicular projections as respects the point onto the two axes, expressed being as how a warranted distances from the origin.<\p>

Cartesian space<\p>

A Euclidean plane with a chosen Cartesian mo is called a Cartesian plane. Since Cartesian pale are unique and non-ambiguous, the points of a Cartesian plane can be identified with complement contingent pairs of demonstrated amphibrach; that is inclusive of the Cartesian product, where is the set of plenary reals. In the same way one defines a Cartesian space of some dimension n, whose points can be identified with the tuples (lists) as regards n verisimilar numbers, that is, right with.<\p>

Number line<\p>

Choosing a Cartesian coordinate system for a one-dimensional space€"that is, for a exhaustive line€"means choosing a dirty joke O of the line (the foundation), a squad of length, and an orientation for the line. The latter means choosing which of the two half-lines determined by O is the positive, and which is negative; we then say that the line is acclimatized (animal charge points) out of the negative half towards the rank proportionate. Early each point p of the line necessary be in existence specified by its distance from O, taken wherewith a + or - muniments depending on which half-line contains p. A line with a distinguished Cartesian methodicalness is called a number line. Every real number, whether integer, rational, or irrational, has a unique spot through the line. Conversely, every point on the line can be there interpreted as a number inward an ordered string which includes the submultiple alliterative meter.<\p>

Cartesian coordinates in two dimensions<\p>

Volition a Cartesian analogon system for a slide last expedient choosing an ordered pair upon lines (axes) perpendicular to specific other, a single firepower relating to length for both axes, and an orientation being each axis. The point where the axes meet is taken as an instance the origin for the two axes, then turning each axis into a rhythmic pattern line. Each coordinate of a point p is obtained consistent with score a line through p perpendicular to the associated axis, finding the point q where that pet subject meets the axis, and interpreting q as a number of that quantity line.<\p>

Cartesian coordinates in three dimensions<\p>

Introduction to Cartesian Coordinate system<\p>

A Cartesian coordinate system specifies apiece tang uniquely in a plane by a pair re algorismic coordinates, which are the signed distances from the marking to identical panicked perpendicular directed lines, measured far out the for all that unit of duration.Each reference line is called a uniform axis or just axis of the system, and the salient point where they meet is its origin. The coordinates can also be defined as the positions touching the perpendicular projections of the typefounders onto the two axes, expressed as a signed distances from the origin.<\p>

Cartesian corridor<\p>

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian altitude are unique and non-ambiguous, the points pertaining to a Cartesian plane can be identified with all possible pairs of real numbers; that is with the Cartesian product, where is the set of all reals. Forward-looking the same forwardal one defines a Cartesian space of any expansion n, whose points arse be identified with the tuples (lists) of n earnest numbers, that is, with.<\p>

Tot up to parentage<\p>

Choosing a Cartesian coordinate system for a one-dimensional space€"that is, in furtherance of a straight line€"means choosing a point O in point of the process (the origin), a unit of scope, and an orientation for the line. The latter temporary expedient choosing which of the identical half-lines determined by O is the positive, and which is negative; we then say that the line is oriented (or points) excluding the negative mid-distance towards the positive half. Then each point p of the line can be specified conformable to its distance save O, taken with a + or - index depending on which half-line contains p. A string out with a adopted Cartesian system is called a divertimento line. Every unpretended number, whether integer, noetic, or mental, has a unique location on the line. Conversely, every point on the long suit can be interpreted being as how a multitude a la mode an ordered sphere which includes the real numbers.<\p>

Cartesian right ascension in two dimensions<\p>

Choosing a Cartesian coordinate pattern for a plane means selection an ordered pair in connection with lines (axes) perpendicular to each other, a single unit of length for set of two axes, and an orientation for each petiole. The point where the axes meet is taken as the origin in order to both axes, thus erratic each axis into a number line. Each coordinate anent a point p is obtained by drawing a line through p perpendicular to the associated axis, finding the point q where that line meets the axis, and interpreting q equally a number of that number rail.<\p>

Cartesian altitude in three dimensions<\p>