Some advice for buying a computer

The 12 ^nd of October
SOME ADVICE FOR BUYING A COMPUTER

LESSON WORK
Complete the rules.

- Must have to should are used with infinitive to talk about obligation, things that are necessary to do, or to give advice about things that are a good idea to do.

- They are cannot change their forms in all persons, except we don't add an 'S' in third person.
PRACTICE

1. Grammar

Complete sentences using should, must or have to with the verb in brackets.
a. It has been required that he should read his paper at the seminar.

b. After finding the solution, we must say that axiom and its properties are important enough.

c. Scientists should develop this branch of mathematics, I think.

d. She must summarize the result before she reports it to her boss.

e. You must distinguish between maths objects e.g. numbers, sets of numbers, functions, mappings, transformations, etc.

f. The two rays of an angle should not lie on the same straight line.

g. I think you easiest way should illustrate this problem in the figure. This may be the easiest way.

h. In geometry, set notation and language should clarify matters.

i. A polygon must not have less than 3 segments.
PRACTICE

1. Fill in the gaps using a modal + have + past participle
a. Algebraic formulas for finding the volumes of cylinders and sphere must have been used in Ancient Egypt to compute the amount of grain contained in them.

b. The discovery of the theorem of Pythagoras should have hardly made by Pythagoras himself, but it was certainly made in his school.

c. Regardless of what mystical reasons must have motivated the early Pythagorean investigators, they discovered many curious and fascinating number properties.

d. Imaginary numbers must have been looked like higher magic to many eighteenth century mathematicians.

e. The symbol √ must have been used in the sixteenth century and it resembled a manuscript form of the small r (radix), the use of the symbol √ for square root had become quite standard.

f. Descartes’ geometric representation of negative numbers must have helped mathematicians to make negative numbers more acceptable.

2. Two colleagues are rearranging a meeting. Complete the conversation with: can / can’t, be able to / been able to and then work in pairs to practice the dialogue.
Helen: Jane, I’m afraid that I won’t be able to see you on Friday. I’ve got to see some clients and they can't make it any other time.

Jane: Don’t worry, we can easily meet next week. How would Tuesday morning suit you?

Helen: That’s fine. I can come and pick you up at the station.
HOMEWORK

Pythagorean property

Comprehension check
1. Which sentences in the text answer these questions.

a. The Greeks succeeded in finding other sets of three numbers which gave right triangles and were able to tell without drawing the triangles which ones should be right triangles.

b. The Greek philosopher and mathematician Pythagoras.

c. Pythagorean Property true for all right triangles.

d. To prove that c² = a² + b² for a triangle, it is necessary to construct two squares with dimensions a + b on each side as shown.

e. Each of the four triangles being congruent to the original triangle, the hypotenuse has a measure c.

2. Choose the main idea of the text.

c. The Greek mathematician, Pythagoras contributed to maths history his famous theorem which was proved to be true for all right triangles.

EXTRA TASK FOR SELF-STUDY
Prove the Pythagorean Theorem using numbers.
A triangle with sides 3 cm, 4 cm, 5 cm is a right-angled triangle. Similarly, if we draw a right-angled triangle with shorter sides 5 cm, 12 cm and measure the third side, we find that the hypotenuse has length ‘close to’ 13 cm. To understand the key idea behind Pythagoras’ theorem, we need to look at the squares of these numbers.
Y ou can see that in a 3, 4, 5 triangle, 9 + 16 = 25 or 3² + 4² = 5² and in the 5, 12, 13 triangle, 25 + 144 = 169 or 5² + 12² = 13².

We state Pythagoras’ theorem:

• 
  The square of the hypotenuse of a right-angled
  

triangle is equal to the sum of the squares

of the lengths of the other two sides.

• 
  In symbols c² = a² + b²