Hi Emile,
Here is what we discussed last week:
Geometry: Aug 25 (due by Wed, Aug 27). Read paragraph 22. Solve exercise 51 and write down your solution.
For the proposition: "If a whole number is divisible by 3 then the sum of its digits is divisible by 9," write down the converse proposition.
For each of the direct and converse proposition, if it is true, prove it, and if its is false, give an example where it is false. Write down the proofs and examples.
Added on Tue: Give an example of two angles whose halves add up to 90 degrees, but whose bisectors are not perpendicular.
In your solution to the 2nd question in exercise 51, find where you use the hypothesis that the angles are supplementary.
Algebra: (due by Th, Aug. 28). Section 10. Write down solutions of Problems 31--33. Hint for 31: Start with designating a multiplication to be performed last.
If done with 31--33, try the variant of Problem 31 with 6 numbers to multiply.
Geometry: (due by Mon, Sept 1).
Read paragraph 31. Write down definitions:
- of a broken line, its sides, and its vertices;
- of a convex broken line;
- of a closed broken line.
Draw an example that satisfies the definition, and another example that does not (for instance, draw an example of a closed broken line and of a broken line that is not closed). Solve exercise 53.
Since Monday, Sept. 1 is Labor Day, may I suggest that you spend enough time on Sat, Sun, and Mon to finish all this before school resumes on Tue?
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Here Sasha and Emile study Gelfand-Shen's Algebra and Kiselev's Geometry.
11 comments:
Privet, Emile!
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I just wwanted to do geometry for thursday but i just dont exactly get itwhen it says draw an example....
Hi Emi,
Please be more accurate when you ask something, because otherwise I am not sure what assignment you refer to.
There are three places where I ask to give an example, one place where I ask to draw an example but
no places where Th is mentioned.
Which oen you mean?
thursday meaning due mon sept 1
Ok, thanks!
For each of the three definitions,
it asks to draw an example of a line
that satisfies it, and another one
that does not.
In fact, I ma not sure if this helps because you didn't ask me any question.
There is a story about a famous physicist Paul Dirac. Once he was giving a talk at a seminar covering the blackboard with formulas. At the and the leader of the seminar suggested, as usual, that people in the audience ask questions. One person said: "I don't understand
the formula in the right upper corner of the board." Paul Dirac
stood silent. After a miniute of silence the leader said to him:
"Please, answer the question."
Dirac replied: "I cannot anser, because there was no question , it was a statement. "
So, according to Dirac, saying
"I don't understand something" is merely a statement but not a question, and so cannot be answered.
A broken line is made of several straight segments such that the endpoint of the 1st is the beginning of the 2nd, the end of the 2nd is the beginnig of the 3rd, and so on. These segments are called sides of the broken line, and the endpoints where they connect are called vertices of the broken line.
A broken line is called convex if the sides of the broken line lays on one side of every given side extended into a straight line
How about this:
A broken line is convex if it lies on one side of every side extended to a straight line.
A closed broken line is a broken line that has it's
endpoints coincide.
a broken line is called convex if it lies on one side of every side extended to a straight line
Good! Now answer (finally!) the question why a broken line
that intersects itself cannot be convex.
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