Irrational numbers_video TED talk

What was Hippasus's crime?

• Murdering guests

• Disrupting a sacred ritual

• Discovering irrational numbers

• None of the above

Answer explanation

Hippasus's crime was discovering irrational numbers, which disrupted established mathematical beliefs.

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According to the Pythagorean mathematicians, what is the role of numbers in the universe?

• They are the building blocks of the universe

• They have no significance in the universe

• They are only relevant in music and morals

• They are used to describe eternal rules

Answer explanation

Numbers are the building blocks of the universe, according to Pythagorean mathematicians. They describe eternal rules.

How did Hippasus attempt to prove that the square root of two cannot be expressed as a ratio of two integers?

• By multiplying both sides of the equation by q

• By assuming that p and q have no common factors

• By squaring both sides of the equation

• By substituting p = 2a into the equation

Answer explanation

Hippasus proved that the square root of two cannot be expressed as a ratio of two integers by squaring both sides of the equation.

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What did Hippasus conclude from his proof?

• The gods appreciated his discovery

• The square root of two can be expressed as a ratio of two integers

• The square root of two is a rational number

• No such ratio exists for the square root of two

Answer explanation

Hippasus concluded that no ratio exists for the square root of two.

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How did Hippasus's discovery revolutionize mathematics?

• It disproved the Pythagorean worldview

• It introduced the concept of irrational numbers

• It explained the significance of ratios in music and morals

• It provided a new method for plotting numbers on a number line

Answer explanation

Hippasus's discovery introduced irrational numbers, revolutionizing mathematics.

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What is the relationship between decimals, ratios, and numbers?

• Decimals and ratios are the only ways to express numbers

• Decimals and ratios have no relationship to numbers

• Numbers can only be expressed as decimals or ratios

• Decimals and ratios are different ways to express numbers

Answer explanation

Decimals and ratios are different ways to express numbers

How is the irrational number pi represented?

• As an approximation like 22/7 or 355/113

• As the ratio of a circle's circumference to its diameter

• As a decimal that can be precisely expressed

• As a rational number that can be written as a ratio

Answer explanation

The irrational number pi is represented as the ratio of a circle's circumference to its diameter.

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