PRELIM 01 - Sequences and Series, Nature of Math Flashcards

1
Q

Is a succession of numbers (called terms) that follow a given rule

A

Sequence

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2
Q

A recurrence relation together with the first term of a sequence

A

Inductive definition

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3
Q

In __________, the difference between any two consecutive terms is always the same

A

Arithmetic sequence

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4
Q

Other name for arithmetic sequence

A

Arithmetic progression

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5
Q

The sum of all the terms of a sequence

A

Series

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6
Q

A famous mathematician that was asked by his teacher to add together every whole number from one to a hundred

A

Karl Friedrich Gauss

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7
Q

Greek symbol that means ‘the sum of’

A

Σ (sigma)

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8
Q

The sum of the terms of an infinite geometric sequence

A

Geometric series

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9
Q

Is a sequence of quantities whose reciprocals form an arithmetic progression

A

Harmonic progression

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10
Q

The ancient Greeks considered the __________ to be the most aesthetically pleasing of all rectangular shapes

A

Golden rectangle

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11
Q

The golden rectangle was used many times in the design of the famous Greek temple, the __________

A

Parthenon

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12
Q

Mathematician who realized the advantages of the Hindu-Arabic system

A

Fibonacci

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13
Q

Place where Fibonacci was born

A

Pisa, Italy

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14
Q

Year when Fibonacci was born

A

1175 AD

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15
Q

Full name of Fibonacci

A

Leonardo of Pisa/Leonardo Bigollo

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16
Q

Were introduced in “The Book of Calculating”

A

Fibonacci numbers

17
Q

Arises from the Fibonacci numbers

A

Golden Ratio

18
Q

Golden ratio is represented by the Greek letter __________

A

Phi (Φ)

19
Q

Ratio of Phi

A

1:1.618 or 0.618:1

20
Q

He showed how to find the golden section of a line

A

Euclid

21
Q

Used the golden section to place the f-holes in his famous violins

A

Stradivari

22
Q

Used the golden section to construct the contour and arch of violins

A

Baginsky

23
Q

Tool invented by Dr. Eddy Levin

A

Golden mean gauge