Exploring Patterns and Quasi-Crystals

Exploring Patterns and Quasi-Crystals

Assessment

Interactive Video

Mathematics, Science, History

9th - 12th Grade

Practice Problem

Hard

Created by

Sophia Harris

FREE Resource

The video explores the history and significance of aperiodic tiling patterns, starting with Johannes Kepler's early work on planetary orbits and platonic solids. It delves into Kepler's conjecture on sphere packing and his observations on snowflake geometry. The video then transitions to the discovery of aperiodic tiling patterns by Roger Penrose, which led to the understanding of quasi-crystals. These patterns, once thought impossible, reveal a new kind of symmetry in nature. The video concludes with a sponsorship message from LastPass.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What was Kepler's initial model of the solar system based on?

Nested cubes

Nested spheres separated by platonic solids

Concentric circles

Randomly placed planets

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What did Kepler conjecture about the packing of spheres?

They cannot be packed efficiently

They can be packed in a hexagonal close packing

They can be packed in a cubic arrangement

They can be packed in a triangular arrangement

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What was Wang's conjecture about tiling?

Only square tiles can tile the plane periodically

Tiles cannot tile the plane at all

If tiles can tile the plane, they can do so periodically

All tiles can tile the plane non-periodically

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many tiles did Roger Penrose reduce the aperiodic tiling set to?

Five

Two

Four

Three

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What unique property do Penrose tiles exhibit?

Six-fold symmetry

Three-fold symmetry

Five-fold symmetry

Four-fold symmetry

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What ratio is found in the pattern of kites and darts?

The silver ratio

The golden ratio

Euler's number

Pi

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What did Steinhardt and his students discover about atomic structures?

Atoms form cubic structures

Atoms form tetrahedrons

Atoms form icosahedrons

Atoms form hexagonal structures

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