Constructible numbers

(1)

Constructible numbers

Season 3

Episode 06 Time frame 1 period

Prerequisites :

^General^rulesând^methodsôf^rulerândômpass^geometry

Objectives :

•

^Disover ^the ônept ôf ôntrutible^numbers ând ^study â^few êxamples.

Materials :

•

^T^ask ^sheet.

•

^Answer^sheet.

1 – The basic operations 15 mins

Students are working ingroupsof 3 or4. They haveto nd out the methodtoonstrut

the following quantities, fromthe unit

1

^and ^two ^onstruted ^numbers

a

^and

b

^:

• a + b

^;

• a − b

^;

• ab

^;

• ^a ^b

^;

• √ a

^.

Methods must be shown on the same answer sheet aspart 2.

2 – Some special numbers 40 mins

Still working in groups,students have to onstrut the following numbers. At the end of

the hour,an answer sheet by group must begiven to the teaher tobemarked.

5 3

2 7

√ 2 √

3 √ 2 + √

3 √

3 − √

2 5

3 √ 2 2 7

√ 3

√ 2 × √ 3

√ 2 2

1 √ 2

√ 3 2 1 + √

5 ϕ = 1 + √

5 2

1 ϕ

− 1 + √

5

2

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Document Answer sheet

Part 1 – Methods

Sum of two numbers a + b

b b

b 1 b

b a b

b

Difference of two numbers b − a

b b

b 1 b

b a b

b

Product of two numbers a × b

b b

b 1 b

b a b

b

Quotient of two numbers b/a

b b

b 1 b

b a b

b

Square root of a number √ a

b b

b 1 b

a

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Part 2 – Construct some numbers

1 ^b ^b

5 3

b

2 7

b

√ 2 ^b

√ 3 ^b

√ 2 + √

3 ^b

√ 3 − √

2 ^b

5 3

√ 2 ^b

2 √

3 ^b

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√ 2 × √

3 ^b

√ 2 2

b

1 √ 2

b

√ 3 2

b

1 + √

5 ^b

ϕ = 1 + √ 5 2

b

1 ϕ

b

− 1 + √ 5 2

b

(5)

Document 1

Ânswers ^-^to ^be ^printed ônâ transparent sheet of paper

1 ^b ^b

5 3

b b

2 7

b b

√ 2 ^b ^b

√ 3 ^b ^b

√ 2 + √

3 ^b ^b

√ 3 − √

2 ^b ^b

5 3

√ 2 ^b ^b

2 √

3 ^b ^b

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√ 2 × √

3 ^b ^b

√ 2 2

b b

1 √ 2

b b

√ 3 2

b b

1 + √

5 ^b ^b

ϕ = 1 + √ 5 2

b b

1 ϕ

b b

− 1 + √ 5 2

b b

Constructible numbers