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#1 Re: Exercises » Non - Routine Algebra » 2024-11-14 20:55:19
Hello! I'm back...for now. I'm going to try and stick around for a bit more.
Correct answer, Bob! Woop woop 
Question 8
The following diagrams show the first four steps in forming the Sierpiński triangle.
Diagram because I've forgotten how images work
Step 1: Start with an equilateral triangle of side length 1 unit.
Step 2: Subdivide it into four smaller congruent equilateral triangles and colour the
central one blue.
Step 3: Repeat Step 2 with each of the smaller white triangles.
Step 4: Repeat again.
The question has 3 parts (fancy, fancy):
a. How many white triangles after n steps?
b. Side length of a white triangle at Step n?
c. Fraction of the area that is still white at Step n?
Have fun 
#2 Re: Jai Ganesh's Puzzles » Algebra » 2023-05-12 22:23:58
Hi ganesh,
#3 Re: This is Cool » Black Hole » 2023-05-12 22:18:53
Hi ganesh,
This was a very informative read. Thank you for posting. I have a few questions
1. Is it possible for a black hole to reach full capacity? If so, what happens?
2. I have heard that within a black hole, time and space exchange positions. What does that mean? Can we go only forwards in space but forwards and backwards in time inside a black hole then?
#4 Re: Coder's Corner » Comics I have drawn during boring classes » 2023-05-12 22:11:45
Boring classes do seem to bring out the creative genius in everybody. Sometimes I wonder if it's intentional?
I once made a whole comic rendering of H G Wells' "The Invisible Man" in a fit of boredom during history class. The teacher was too impressed to be cross, thankfully.
#5 Re: Exercises » Compute the solution: » 2023-05-12 22:06:43
Hi ganesh,
#6 Re: Jai Ganesh's Puzzles » Algebra » 2023-05-12 21:54:39
Hi ganesh,
#7 Re: Jai Ganesh's Puzzles » Algebra » 2023-05-12 21:28:49
Hi ganesh,
#8 Help Me ! » VCE Maths and Careers » 2023-05-12 21:24:16
- CurlyBracket
- Replies: 0
First off - Hello! I'm back!
Recently shifted countries and had to cut down on my leisure internet time drastically. I'm in Melbourne, Australia and I'm still adapting to the education system, public transport and most importantly the climate.
Brr...the Southern Hemisphere really freezes in May, doesn't it?
Anyways, there's something called the "VCE" and "ATAR" system here, and it's very confusing. Most people at school are willing to wait it out until Year 12 to understand it, but I'm trying to absorb everything I can and most sources tend to be very vague about it.
For reference, I'm currently in Year 10 and I'm thinking about pursuing a career in Mathematics or Science (more specifically Astrophysics). I'm a decent student, with A+ in all subjects except Sport Science because I can't be bothered to learn all the bones and muscles of the human body.
Due to some "age requirement" thing, my school has tried to put me in the easiest possible maths class, so I'm absolutely sailing through it. My work is already three weeks ahead of schedule and it gives me plenty of time to study on my own. The teacher's very understanding and lets me do whatever I want in class as long as it doesn't involve napping or origami. In short, my school maths life is good pretty good
What are some good college courses I should aim for? How does ATAR scoring work? What does "Specialist Maths Unit 3&4" mean? Why do people keep talking about and and then seem unable to explain it later (haha)?
Sorry about the long information-driven post, but I'm really glad to be back, and I'm looking forward to helping and being helped again!
#9 Re: Help Me ! » Hello » 2023-05-12 20:45:21
Hi Hannibal Lecter,
I assume that the digits of the three rows are independent of one another, and only one combination can be used to unlock the lock.
Therefore we can treat it as a nine digit number.
Starting right from 000 000 000 upto 999 999 999, there are 10^9 different combinations.
Hope that helps!
#10 Re: Jai Ganesh's Puzzles » Algebra » 2023-05-12 20:32:10
Hi ganesh,
#11 Help Me ! » Folding Papers » 2022-10-07 00:28:40
- CurlyBracket
- Replies: 1
Here's the question:
And here's what I did:
AB = 4
BN = x
In Δ ABN,
(16-x)² = 4² + x²
So, x = 15/2
AN = (16 - x²)
= 17/2
Now, area of ABNMD` = ABCD - ANM
= (4 * 16) - ((1/2) * (15/2 ) * 4)
= 64 - 15
= 49 cm²
Where am I mistaken?
#12 Re: Introductions » New Member - Maths is a game » 2022-08-30 23:54:32
Hi mathscolor,
Welcome to the forum! I hope you have a good time here.
#13 Re: Exercises » Non - Routine Algebra » 2022-08-30 21:06:05
Correct answer! And great explanation too.
Easy one now :
Question 7
There are 3 numbers.
The second is greater than the first by the amount the third is greater than the second.
The product of the two smaller numbers is 85.
The product of the two larger numbers is 115.
If the numbers are x, y, z with x<y<z then the value of (2x + y+ 8z) is?
#14 Re: Exercises » Non - Routine Algebra » 2022-08-29 21:39:14
Ok, done. Thanks, phrontister.
Here’s the next one.
Question 6
The combined age of a man and his wife is six times the combined ages of their children.
Two years ago their united ages were ten times the combined ages of their children.
Six years hence their united ages will be three times the combined ages of the children.
How many children do they have?
#15 Re: Exercises » Non - Routine Algebra » 2022-08-29 19:17:04
Then should I edit it to just say "Who won?"
#16 Re: Puzzles and Games » Hangman 1 » 2022-08-28 17:00:37
I've seen an interesting trend. Most of my classmates use the latest apps and social networks (Discord, Insta, etc etc) but there's a growing population of people who have begun to quit them because they're 'getting too popular'!
It's as if the 'centralization' of the web will ultimately lead to its 'decentralization'.
Eh, people are complicated.
As for you're word, is there a 'T'?
#17 Re: Exercises » Non - Routine Algebra » 2022-08-28 16:45:03
Hi phrontister,
That's the correct answer!
I solved it like this. It's quite similar.
#18 Re: This is Cool » Library of Babel » 2022-08-28 16:18:39
I'm not sure my brother would be happy to be described as lazy
Mycroft did his analysis sitting in an armchair. Physically not much but mentally a tour de force.
Bob
Oopsies! I didn't think of it that way.
Then your brother, who's in the University of Edinburgh, is working on a mathematical fact checker?
That sounds really awesome.
#19 Re: Help Me ! » Trigonometry Table » 2022-07-11 23:02:26
Yes, please!
#20 Re: Help Me ! » Trigonometry Table » 2022-07-11 04:28:32
Ok, got it.
Then the known values for AP will be at 135, 225 and 315.
#21 Re: Exercises » Compute the solution: » 2022-07-10 00:16:10
Hi,
P.S: The same question came in my exam today!
#22 Re: Exercises » Non - Routine Algebra » 2022-07-10 00:10:05
I've got it now! Thanks for the help, Bob and Ganesh!
Here's another question. It's a bit different from the others. Flavours are the essence of life!
Question 5
Three teams of woodcutters have decided to organize a competition. The winner is the team who fells the maximum number of trees in the given time.
The first and third team together felled twice the number of trees felled by the second team.
The second and third team together felled three fold of the number of trees felled by the first team.
Who won? Or in the event of there being joint winners, who would then be named as such?
#23 Re: Help Me ! » Trigonometry Table » 2022-07-09 23:43:28
Hi Bob,
A big THANK YOU!!
Okay, I'll answer the questions now.
(a) What is the largest that AP can ever be?
(b) What is the most negative it can be?
(c) In my image the angle POA is 45 degrees and we know the coordinates. Just based on that and using symmetry for what other angles would you be able to give the distance AP? You should be able to find three possible answers here, one between 90 and 180, and two more where the angle is over 180.
(d) If P goes al the way round and starts a second circle we could record the angle by using numbers over 360. For example, P will be back to my image position when the angle of turn is 360 + 45 = 405. What is the next angle when P is in this position?
(a) 1 unit.
(b) -1 unit.
(c) I'm not about this one. But I know the value for AP at 0, 90, 180 and 270.
(d) 405 + 360 = 765. Oh wait, that sort of explains the Trigonometry Table thing! I see now.
#24 Re: Jokes » Fibonacci » 2022-06-27 02:20:19
Hi Phil,
I'll say this in ganesh's style:
Welcome to the forum!
Good joke
#25 Re: Maths Is Fun - Suggestions and Comments » On improving the "Messaging" subsection of the Profile section » 2022-06-27 02:09:19
Hi,
I know this is a bit of an aside but still - it's surprising how dynamic the world of the internet is.
Personally, I've never heard of these services mentioned above, with the sole exception of AOL, which we use as an inside joke among my friends to describe someone who just can't move on from the old, lives in a shed with a cowboy hat - that sort of thing.
Today's mega giants - Discord, Reddit, YouTube, Instagram, Twitter even outlook or gmail! How long do they have?
I was a five year old when Skype and Yahoo were all the rage. Why did they stop? Why do any of these stop?
Is there a way to determine the decline of a certain app or website?
What are the factors behind this?