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Math 10 (Finals) > MODULE 6: Shapes > Flashcards

MODULE 6: Shapes Flashcards

1
Q

Etymology of Geometry (Greek).

A

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

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2
Q

What does Geometry study?

A

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

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3
Q

Three Mathematics before Euclidean Mathematics

A

Babylonian
Egyptian
Greek

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4
Q

Babylonian Mathematics were written in ______ on _______.

A

Cuneiform
Clay Tablets

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5
Q

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

A

Babylonian

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6
Q

The circumference of a circle according to Babylonian Mathematics.

A

three times the diameter (3D)

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7
Q

The approximation of pi in Babylonian Mathematics.

A

3

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8
Q

The area of a circle according to Babylonian Mathematics.

A

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

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9
Q

First to use the Pythagorean Theorem/Triples.

A

Babylonians

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10
Q

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

A

Egyptian

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11
Q

The Mathematics that discovered irrational numbers.

A

Greek

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12
Q

First mathematician to calculate the circumference of the Earth.

A

Eratosthenes (40,000 km)

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13
Q

Discovered the Pythagorean Theorem.

A

Pythagoras

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14
Q

Contributed to finding the volumes of irregular shapes.

A

Archimedes of Syracuse

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15
Q

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

A

Archimedes of Syracuse

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16
Q

Golden Rectangles

A

rectangle with the most pleasing proportions

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17
Q

responsible for Euclidean Geometry, the mathematical system used globally

A

Euclid of Alexandria

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18
Q

Euclid’s Textbook

A

The Elements

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19
Q

Undefined terms according to Euclid

A

points
lines
planes

20
Q

Axioms are

A

logical mathematical statements that do not need to be proven

21
Q

Euclid’s Five Axioms

A
  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
22
Q

Postulates are

A

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

23
Q

Euclidean Postulates

A
  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
24
Q

Playfair’s Axiom states

A

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

25
Q

What are Euclidean Triangles?

A

Triangles whose interior angles’ sum is always 180 degrees

26
Q

Congruent triangles are

A

Triangles that have the same size and shape

27
Q

Similar triangles are

A

Triangles that have the same shapes and angles but different lengths

28
Q

Three Congruence Criteria for Euclidean Triangles

A

SSS
SAS
ASA

29
Q

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.

A

Hyperbolic Geometry

30
Q

First to publish Hyperbolic Geometry

A

Nikolai Ivanovich Lobachevsky

31
Q

Diameters are

A

line segments passing through the center of the disk

32
Q

Arcs

A

intersect yhe disk at rigt angles

33
Q

Arcs

A

intersect the disk at right angles

34
Q

Model used in Hyperbolic Geometry

A

Poincare’s Disk Model

35
Q

Hyperbolic Triangles

A

Triangles whose interior angles are less than 180 degrees

36
Q

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.

A

Elliptic Geometry

37
Q

The model used in Elliptic Geometry

A

Spheres with great circles

38
Q

Studied Elliptic Geometry

A

George Friedrich Bernhard Riemann

39
Q

Elliptic Triangle

A

Triangles whose interior angles are more than 180 degrees

40
Q

Topology is

A

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

41
Q

Responsible for Topology

A

Jules-Henri Poincare

42
Q

Topological Transformation includes

A

stretching
shrinking
twisting
bending

43
Q

Topological Transformation does not include

A

cutting
tearing
puncturing
merging

44
Q

Topologically equivalent

A

same number of holes

45
Q

Homeomorphism

A

equivalence

46
Q

Homeomorphic

A

when shapes are topologically equivalent to each other

Math 10 (Finals) (4 decks)

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