Mathematics in Our World – Key Concepts

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These flashcards review the lecture’s central ideas: the nature of mathematics, common natural patterns and their properties, Fibonacci sequence basics, and the precision of mathematical language.

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22 Terms

1
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What are the two main cognitive abilities required in mathematics?

Logical thinking/problem-solving and creative/abstract thinking.

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4
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Complete the quote: “Mathematics is the __ with which God has written the universe.”

language

5
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Define a pattern in the context of nature.

A visible, regular form or sequence found in the natural world that can often be modeled mathematically.

6
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What special line divides an object into two identical halves in bilateral symmetry?

Line of symmetry (mirror line).

7
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Give an example of bilateral symmetry in living things.

Human body, orchid flower, or a leaf with two identical halves.

8
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How is radial symmetry different from bilateral symmetry?

Radial symmetry has more than two identical parts arranged around a central point, whereas bilateral symmetry has two mirrored halves.

9
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Explain cyclic symmetry and give one example.

Symmetry with rotation only; rotating the figure about the center leaves it unchanged. Example: a 5-armed starfish (C₅ symmetry).

10
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Explain dihedral symmetry and give one example.

Symmetry that combines rotation and reflection; the object can be rotated and reflected across mirror lines. Example: a snowflake (D₆ symmetry).

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What is the defining property of a fractal?

Self-similarity—the same shape repeats at different scales.

12
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Why are natural fractals considered only approximate?

Infinite iteration is impossible in nature, so real-world fractal patterns terminate after several levels.

13
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Describe a spiral in mathematical terms.

A curve that emanates from a point and moves farther away as it revolves around that point.

14
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How is the Fibonacci sequence generated?

Each term after the second is the sum of the two preceding terms.

15
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Write the next two terms of the Fibonacci sequence 1, 1, 2, 3, 5, 8, __, __.

13, 21

16
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What is tessellation?

A pattern formed by repeating tiles that cover a flat surface without gaps or overlaps.

17
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Why do soap bubbles form spheres?

A sphere has the minimal surface area for a given volume, minimizing surface tension.

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What adaptive advantage do animal stripe patterns often provide?

Camouflage or signaling that increases offspring survival and reproduction chances.

19
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What information can crack patterns reveal about a material?

Whether the material is elastic or not, based on how it relieves stress.

20
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State three characteristics of mathematical language.

Precise, concise, powerful.

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In mathematical language, what corresponds to an English noun?

A mathematical expression (it names a quantity or object but does not make a complete statement).

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What is the mathematical analogue of an English sentence?

A mathematical sentence (an equation or inequality that states a complete thought).