SHR-1 Smoleho Ivan

Dimension – размерность
Plane – плоскость
Solid – пространство
Cartesian coordinate system – Декартова
(прямоугольная) система координат
Polar Coordinates – полярные координаты
frame of reference – система отсчёта
geometric locus – геометрическое место точек

3.

Attitude – отношение
centaur – кентавр
Laymen – обыватель
breadth – ширина
Sufficient – достаточный
duration – протяжённость
to preclude –
merit – преимущество
препятствовать
rectangular – прямоугольный
magnitude – величина
quantity – количество
longitude – долгота
subsequent – последующий
latitude – широта
curvature – кривизна
refer – упоминать,
pictorially – графически
относиться
convenient – удобный

4.

equations – уравнения
Assert – утверждать
obtains – получать
Loci – место
stems – побеги
Manifold – множество
Cartesian coordinate system –
Nebulous – смутный
Декартова система координат
Vague – неопределённый
Intractable –
frame of reference – система
трудноразрешимый
отсчёта (координат)
Skillfully – умело
customary – обычный
Treatise – трактат
oblique – наклонный
Derived – выведенный
intersection – пересечение

5.

presuppose – предполагать
Hence – следовательно
correspondence –
Portion – доля
соответствие
Transverse - поперечный
namely – именно
properties – свойства
define – определять
totality – совокупность
slope – наклон
denoted – обозначенный
principal – главный, основной

6.

General questions:
Is it possible to imaging a four-dimensional figure?
Does the hyperbola intersect the vertical axis?
Special questions:
Which equation defines a parabola?
How many foci does an ellipse have?
Subject questions:
Who first proposed the use of polar coordinates?
What role did Joseph Louis Lagrange play in the development of fourdimensional geometry?
Tag questions:
There is a correspondence between geometric locus and equations, isn't there?
Four-dimensional geometry was undeveloped until the 20th century, wasn’t it?
Alternative questions:
Did Ptolemy admit the existence of four-dimensional space or deny it?
Did Isaac Newton introduce the concept of polar coordinates before or after
Jakob Bernoulli?

7.

In the fourteenth century N. Oresme sought a
graphic representation of Aristotelian forms as
heat, velocity, sweetness and so on by laying down
a line as a basis, called a longitude, and taking one
of the forms to be represented by lines
perpendicular to this as a latitude. The form was
then represented by a surface. Taking a surface as
a basis, with latitude perpendicular at each point, a
solid was formed. He even went on to take a solid
as a basis and at each point considered an
increment. But he rejected a fourth-dimensional
figure out of hand and considered instead the solid
as consisting of infinitely many planes. Taking
perpendiculars at each point of each plane, the
result was an infinite set of intersecting solids.
However, he did use the phrase “fourth
dimension”

8.

Polar Coordinates. Points are most commonly
described today by ordered pairs (x, y) in the
Cartesian system, where x is the directed
distance from the vertical axis and у is the
directed distance from the horizontal axis. For
certain kinds of curves, however, a more
convenient and useful form of representation is
that of polar coordinates. The polar ordered
pair is (r, Ө), where Ө is the angle the vector
makes with the reference line or polar axis and
r is the length of the vector.

9.

Thus, we define a curve as composed of points
whose coordinates satisfy a certain equation.
We may think of a curve as a locus or a path
traced by a moving point according to certain
specified conditions. From these conditions it is
possible to derive the equation of its curve and
then discuss the curve in detail from the
equation. The locus of an equation in X and Y is
defined as the totality of points whose
coordinates satisfy the equation. There exists
no definite rule for finding the equation of the
locus. As a matter of fact the problem is to
translate the geometric definition o f the locus
into an algebraic form with a suitable choice of
a coordinate system.

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