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Math 10 > Lecture Note 6 > Flashcards

Lecture Note 6 Flashcards

1
Q

he was known to be the first mathematician to calculate the circumference of the earth

A

erathosthenes

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2
Q

he gave us the most popular version of the Euclid’s 5th postulate

A

playfair

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3
Q

The point of intersection is called the?

A

center of perspectivity

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4
Q

Two triangles are ___________ if they have the same shape but can be different sizes

A

Similar

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5
Q

Gerard considered the concept of parallel line intersecting in a plane and called this the?

A

ideal point

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6
Q

The model of this geometry conceived by the great universal mathematician Henri Poincare is now called the?

A

Poincare Disk of Hyperbolic Geometry

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7
Q

other term for golden ratio

A

divine proportion

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8
Q

published his work on this geometry first in an article entitled “Geometrische Untersuchungen zur Theorie der Parellenien
(Geometrical Researches on the Theory of Parallels)” in 1829

A

Lobachevsky

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9
Q

elliptic geometry was studied deeply by the German mathematician _____________________________________

A

George Friedrich Bernhard Riemann

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10
Q

he was another Greek mathematician who contributed a handful geometric concepts like the volumes of irregular shapes

A

archimedes

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11
Q

includes the mathematical study of vanishing
points and perspective

A

projective geometry

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12
Q

it is concerned with the properties of space that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing

A

topology

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13
Q

mathematicians who restated Euclid’s 5th postulate

A

posidonius, proclus, legendre

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14
Q

A model for the hyperbolic geometry can be seen by considering not the usual plane,
but a?

A

circular disk

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15
Q

In _________________, we consider geometry as the theory of space of points

A

Topology

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16
Q

this is synonymous with the term axiom

A

postulate

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17
Q

This geometry existed for quite some time before Euclid formalized it in his book “The Elements”

A

Euclidean geometry

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18
Q

they were the main contributors
of Hyperbolic geometry

A
  • Nikolai Ivanovich Lobachevsky (Russian mathematician and
    geometer)
  • Janos Bolyai (Hungarian mathematician)
  • Johann Carl Friedrich Gauss (German mathematician)
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19
Q

it is all about discovering and analyzing the essential similarities and differences between sets and figures

A

topology

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20
Q

Two Euclidean triangles are ______________ if and only if they have the same size and shape.

A

Congruent

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21
Q

This shape, caused by the flattening at the poles, is called an?

A

oblate spheroid

22
Q

The sum of the angles of a (hyperbolic) triangle are?

A

less than 180

23
Q

method of exhaustion developed by?

A

Eudoxus of Cnidus

24
Q

known as the father of projective geometry

A

Gerard Desargues

25
Q

gave us the concept that given a right triangle with lengths of sides a and b; and, length of side opposite the right angle is c, then a2 + b2 = c2

A

Pythagoras

26
Q

Alexander Henry Rhind purchased the papyrus in?

A

1885 in Luzor, Egypt

27
Q

method of finding area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the
containing shape

A

method of exhaustion

28
Q

He stated that any two lines on a plane intersect. This gave rise to the creation of?

A

projective geometry

29
Q

he published a book entitle “Vorstudien zur Topologie (Introductory Studies to Topology)” having this notion of space and geometry in a symmetric development

A

Jules-Henri Poincare

30
Q

it deals with points and set of points

A

geometry

31
Q
A
32
Q

________________ of Alexandria was one of the most famous Greek mathematician

A

Euclid

33
Q

One main idea is ____________________________ that include stretching, shrinking, twisting or bending the figure in any way that allows the points to remain distinct

A

Topological Transformations

34
Q

Other consequences of Euclid’s Axiomatic System on triangles are on?

A

congruency and similarity

35
Q

Through a point P not on a line l , there exists exactly one line passing through a point P parallel to l .

A

playfair’s axiom

36
Q

The sum of the angles of a (elliptic) triangles are?

A

more than 180

37
Q

One of the most significant contributions of the Greek was the discoveries of?

A

irrational numbers and golden ratio

38
Q

They used this geometry to create works of art having three-dimensional perspective

A

projective geometry

39
Q

Two triangles ABC and abc are perspective from a line l if corresponding sides of the triangles meet at points on l , called the?

A

axis of perspectivity

40
Q

textbook of Euclid

A

The Elements

41
Q

the most popular version of the Euclid’s 5th postulate is now called?

A

playfair’s axiom

42
Q

concept of Pythagoras

A

Pythagorean theorem

43
Q

There are concepts in geometry which are called?

A

undefined terms

44
Q

These formulas are recorded in the famous

A

Ahmes Papyrus (also known as the Rhind Mathematical Papyrus)

45
Q

Two figures are called __________________________ if one figure can be stretched, shrunk, twisted or bent into the same shape as the other

A

Topologically Equivalent

46
Q

By assuming the negation of Euclid’s 5th Postulate, we get a new geometry called

A

hyperbolic geometry

47
Q

a French mathematician and engineer, revisited Euclid’s second postulate: A finite straight line can be produced continuously in a straight line.

A

Gerard Desargues

48
Q

it is the oldest geometry

A

Euclidean Geometry

49
Q

Rhind Papyrus was named after

A

Alexander Henry Rhind

50
Q

a Scottish antiquaria, who purchased the papyrus in 1858 in Luzor, Egypt

A

Alexander Henry Rhind

51
Q

The 5th Postulate is also called the?

A

parallel postulate

52
Q

He was also known for deriving an accurate approximation of the value of π using the method of exhaustion developed by Eudoxus of Cnidus.

A

archimedes

Math 10 (3 decks)

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