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Hi,
Thanks ganesh. I think I forgot to but the negative symbol in the last question.
Anyway, here's the next one:
There! I've done fractions without LaTeX!
Hi,
I have recently begun to learn trigonometry. I learnt the trigonometry table yesterday. However, I have a few major issues with it.
1. Why does the table begin at 0°? I know that θ is a angle of a triangle. And I know from my previous chapters that no triangle can have a 0° angle. Then how can θ be 0 in any case?
2. Why is there a 90° angle? Since trigonometry is about right-angled triangles, then this would mean the other angle is 0° (by sum of interior angles property), which, as I have stated before, I have learnt to be impossible.
3. Why are there columns for 180°, 270° and 360°? This would suggest the other angles are negative! Is this even a triangle anymore?
So to summarise, I have a problem with practically every element of the trigonometry table, excluding 30°, 45° and 60°.
It does not seem to agree with any of my previous knowledge at all!
197406
Hi Bob,
Yes, I've added a slightly detailed rule list (only three rules, there aren't many) to the main post.
P.S: I've changed the signature. How is it now?
I recently discovered a really excellent puzzle in the newspaper - it's called Slitherlink or Loop the Loop.
Here's a challenging puzzle. It's only a 6x6, but it'll take a while
https://ibb.co/RSkfcr2
Rules of Slitherlink:
1. You have to make a full closed figure, where the numbers signify the number of lines around it.
2. Empty squares can have any number of lines (or links) around them.
3. There should be no overlappings or branchings of the lines.
I recommend
https://www.conceptispuzzles.com/index.aspx?uri=puzzle/slitherlink/techniques
for Slitherlink techniques.
Hi Ganesh,
That’s an interesting choice. I have asked many people this question and not many came up with this answer. I think I would like to travel some 100 years into the future, into the year 2121 CE. I would like to find out what the developments in space technology and the environment of the Earth will be.
I think travelling will be possible in the future, if not the near future. Some scientists already say that Black Holes are potential time machines.
Here’s my list:
1. Spaceflight Simulator
2. NCTM KenKen
3. Stop Motion
Hi,
Imagine that you have been given a time machine from the future. Which time period would you first visit and why? Do you think such an invention is possible in the near future?
Note: If possible, you can even given an idea as to how you think it might function. This is a personal response question, so there are no right or wrong answers.
Hi Bob,
Latin grammar sounds interesting, I have not had the occasion to encounter it until now. Yes, I do suspect a typographical error.
As for ‘commonly encountered in the Workplace’, I can only guess. Either these Latin proverbs WERE common 95 years ago or the publisher overestimated the number of Latin proverbs the common office-goer is aware of and uses frequently. If I remember rightly, the list included over 120 proverbs, both Latin and of languages other than English such as French and German.
The idea for the signature sounds promising. I’ll try thinking of something along those lines.
Hi everyone,
Thank you for the replies.
From what I understood, then there can be 4 possibilities:
4=5
-4=-5
-4=5
4=-5
None of these are correct.
Am I on the right track?
Here are my answers:
Hi Bob,
Thanks again!
Yes, the difference in spelling is quite possible. I had fished the proverb out of a general dictionary from about 1935 ( to my surprise, the heading was ‘Common, daily life Latin Phrases one encounters each day in the Workplace: A Hand-guide’ although I had not heard of any), so either there was a typographical error or the spelling changed over the years. I suppose the former is far more probable.
Frankly, I never noticed the perspective you’ve given. It’s quite practical, and it makes more sense for it to be ‘Encountered in the Workplace’. I searched for it too, and turns out it’s also used legally!
A humorous phrase just took on a whole new meaning for me!
Fear of long words: Hippopotomonstrosesquippedaliophobia
Fear of Math: Arithmophobia
Fear of Newspapers: Chloephobia
Hi Mathegocart,
That's a nice proverb. I hadn’t heard of it before. It's certainly very true.
Here's another:
Caesar non est supra grammaticos
We use it in modern context as "Knowledge before Power". However, the origin story is very different.
The Roman emperor had made a grammatical mistake in one of his speeches. He became very angry on being corrected, and declared that grammar should be modified in order to match with his statement. At this, the Council replied "Caesar non est supra grammaticos," meaning 'The Emperor is not above Grammar.'
The saying quickly became popular, and we understand it in a slightly modified form today.
Hi,
I came across a proof today, which stated that 1=0. While I don’t agree with the statement, neither can I find the inaccuracy in the proof. Here it is:
-20=-20
16-36 = 25-45
4 ² - 9*4 = 5 ² - 9*5
4 ² - 9*4 + 81/4 = 5 ² - 9*5 + 81/4
(4 - 9/2) ² = (5 - 9/2) ²
4 = 5
4 + 0 = 4 + 1
0 = 1
Thank you, Mathegocart!
Hi Bob!
Thanks for the reply.
From your diagram, I can conclude that:
3x+3y=180
x+y=60
In Δ PMQ:
2x+2y+ ∠M=180
∠M = 180 - 2(x+y)
= 180 - 120. [from (x+y=60)]
= 60
In Δ PNQ:
x+y+ ∠N=180
∠N = 180 - x - y
= 180 - 60
= 120
k N = M
k = M / N
= 60/120
=1/2
Hence, the value of k is 0.5
Exceptio probat regulum!
Which 'rule' do you have in mind?
I normally use this in a humorous situation, where something partially or completely untrue has been said. What about you?
Hi,
I have a question about Parallelograms:
PQRS is a parallelogram. MP and NP divide ∠SPQ into three equal parts (∠MPQ >∠NPQ) and MQ and NQ divide ∠RQP into 3 equal parts (∠MQP > ∠NQP).
If k(∠PNQ) = (∠PMQ) then k = ?
I'm not able to make a suitable diagram to agree with all the criteria of the figure.
Any help will be appreciated.
Thank you, Ganesh!
Thank you, Mathman2022 and zetafunc.
Hello Everyone!
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