Lecture Note 6

Question 1

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

Answer 1

erathosthenes

Question 2

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

Answer 2

playfair

Question 3

The point of intersection is called the?

Answer 3

center of perspectivity

Question 4

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

Answer 4

Similar

Question 5

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

Answer 5

ideal point

Question 6

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

Answer 6

Poincare Disk of Hyperbolic Geometry

Question 7

other term for golden ratio

Answer 7

divine proportion

Question 8

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

Answer 8

Lobachevsky

Question 9

elliptic geometry was studied deeply by the German mathematician _____________________________________

Answer 9

George Friedrich Bernhard Riemann

Question 10

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

Answer 10

archimedes

Question 11

includes the mathematical study of vanishing
points and perspective

Answer 11

projective geometry

Question 12

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

Answer 12

topology

Question 13

mathematicians who restated Euclid’s 5th postulate

Answer 13

posidonius, proclus, legendre

Question 14

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

Answer 14

circular disk

Question 15

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

Answer 15

Topology

Question 16

this is synonymous with the term axiom

Answer 16

postulate

Question 17

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

Answer 17

Euclidean geometry

Question 18

they were the main contributors
of Hyperbolic geometry

Answer 18

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

Question 19

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

Answer 19

topology

Question 20

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

Answer 20

Congruent

Question 21

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

Answer 21

oblate spheroid

Question 22

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

Answer 22

less than 180

Question 23

method of exhaustion developed by?

Answer 23

Eudoxus of Cnidus

Question 24

known as the father of projective geometry

Answer 24

Gerard Desargues

Question 25

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

Answer 25

Pythagoras

Question 26

Alexander Henry Rhind purchased the papyrus in?

Answer 26

1885 in Luzor, Egypt

Question 27

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

Answer 27

method of exhaustion

Question 28

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

Answer 28

projective geometry

Question 29

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

Answer 29

Jules-Henri Poincare

Question 30

it deals with points and set of points

Answer 30

geometry

Question 32

________________ of Alexandria was one of the most famous Greek mathematician

Answer 32

Euclid

Question 33

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

Answer 33

Topological Transformations

Question 34

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

Answer 34

congruency and similarity

Question 35

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

Answer 35

playfair's axiom

Question 36

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

Answer 36

more than 180

Question 37

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

Answer 37

irrational numbers and golden ratio

Question 38

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

Answer 38

projective geometry

Question 39

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

Answer 39

axis of perspectivity

Question 40

textbook of Euclid

Answer 40

The Elements

Question 41

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

Answer 41

playfair's axiom

Question 42

concept of Pythagoras

Answer 42

Pythagorean theorem

Question 43

There are concepts in geometry which are called?

Answer 43

undefined terms

Question 44

These formulas are recorded in the famous

Answer 44

Ahmes Papyrus (also known as the Rhind Mathematical Papyrus)

Question 45

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

Answer 45

Topologically Equivalent

Question 46

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

Answer 46

hyperbolic geometry

Question 47

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

Answer 47

Gerard Desargues

Question 48

it is the oldest geometry

Answer 48

Euclidean Geometry

Question 49

Rhind Papyrus was named after

Answer 49

Alexander Henry Rhind

Question 50

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

Answer 50

Alexander Henry Rhind

Question 51

The 5th Postulate is also called the?

Answer 51

parallel postulate

Question 52

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

Answer 52

archimedes