MODULE 6: Shapes

Question 1

Etymology of Geometry (Greek).

Answer 1

Geo (earth) and Metron (measurement) –> study of Earth’s measurement

Question 2

What does Geometry study?

Answer 2

sizes, shapes, angles, positions, and dimensions of things

Question 3

Three Mathematics before Euclidean Mathematics

Answer 3

Babylonian
Egyptian
Greek

Question 4

Babylonian Mathematics were written in ______ on _______.

Answer 4

Cuneiform
Clay Tablets

Question 5

The Mathematics that gave us formulas on the areas and volumes of circles and cylinders.

Answer 5

Babylonian

Question 6

The circumference of a circle according to Babylonian Mathematics.

Answer 6

three times the diameter (3D)

Question 7

The approximation of pi in Babylonian Mathematics.

Answer 7

3

Question 8

The area of a circle according to Babylonian Mathematics.

Answer 8

1/12 of C^2 (square of the circumference)

Question 9

First to use the Pythagorean Theorem/Triples.

Answer 9

Babylonians

Question 10

Gave us formulas in finding areas and volumes that they used in constructing pyramids and determining food supply.

Answer 10

Egyptian

Question 11

The Mathematics that discovered irrational numbers.

Answer 11

Greek

Question 12

First mathematician to calculate the circumference of the Earth.

Answer 12

Eratosthenes (40,000 km)

Question 13

Discovered the Pythagorean Theorem.

Answer 13

Pythagoras

Question 14

Contributed to finding the volumes of irregular shapes.

Answer 14

Archimedes of Syracuse

Question 15

Accurately approximated the value of pi using the method of exhaustion developed by Eudoxus of Cnidus.

Answer 15

Archimedes of Syracuse

Question 16

Golden Rectangles

Answer 16

rectangle with the most pleasing proportions

Question 17

responsible for Euclidean Geometry, the mathematical system used globally

Answer 17

Euclid of Alexandria

Question 18

Euclid’s Textbook

Answer 18

The Elements

Question 19

Undefined terms according to Euclid

Answer 19

points
lines
planes

Question 20

Axioms are

Answer 20

logical mathematical statements that do not need to be proven

Question 21

Euclid’s Five Axioms

Answer 21

1. Things that are equal to the same things are equal
2. If equals are added to equals, then the wholes are equal
3. If equals are subtracted from equal, then the remainders are equal
4. Things that coincide with one another are equal to another
5. The whole is greater than the part

Question 22

Postulates are

Answer 22

Mathematical statements are considered true as long as it is not disproven.

Question 23

Euclidean Postulates

Answer 23

1. A straight line can be drawn from any point to any point
2. A finite straight line can be produced continuously in a straight line
3. A circle may be drawn with any point as the center and any distance as a radius
4. All right angles are equal to one another
5. Parallel Postulate

Question 24

Playfair’s Axiom states

Answer 24

Only one line that passes through point P can be parallel to line I

Question 25

What are Euclidean Triangles?

Answer 25

Triangles whose interior angles' sum is always 180 degrees

Question 26

Congruent triangles are

Answer 26

Triangles that have the same size and shape

Question 27

Similar triangles are

Answer 27

Triangles that have the same shapes and angles but different lengths

Question 28

Three Congruence Criteria for Euclidean Triangles

Answer 28

SSS SAS ASA

Question 29

A Non-Euclidean Geometry that negated Euclid's 5th postulate and allowed curved lines, and assumed that there can be at least two lines through point P parallel to line I.

Answer 29

Hyperbolic Geometry

Question 30

First to publish Hyperbolic Geometry

Answer 30

Nikolai Ivanovich Lobachevsky

Question 31

Diameters are

Answer 31

line segments passing through the center of the disk

Question 32

Arcs

Answer 32

intersect yhe disk at rigt angles

Question 33

Arcs

Answer 33

intersect the disk at right angles

Question 34

Model used in Hyperbolic Geometry

Answer 34

Poincare's Disk Model

Question 35

Hyperbolic Triangles

Answer 35

Triangles whose interior angles are less than 180 degrees

Question 36

A Non-Euclidean Geometry that negated Euclid's 5th postulate by proving that there are no parallel lines to I that pass through point P.

Answer 36

Elliptic Geometry

Question 37

The model used in Elliptic Geometry

Answer 37

Spheres with great circles

Question 38

Studied Elliptic Geometry

Answer 38

George Friedrich Bernhard Riemann

Question 39

Elliptic Triangle

Answer 39

Triangles whose interior angles are more than 180 degrees

Question 40

Topology is

Answer 40

The study of space where there are abstract relations of points and geometry is seen as the theory of space of points

Question 41

Responsible for Topology

Answer 41

Jules-Henri Poincare

Question 42

Topological Transformation includes

Answer 42

stretching shrinking twisting bending

Question 43

Topological Transformation does not include

Answer 43

cutting tearing puncturing merging

Question 44

Topologically equivalent

Answer 44

same number of holes

Question 45

Homeomorphism

Answer 45

equivalence

Question 46

Homeomorphic

Answer 46

when shapes are topologically equivalent to each other