This is bad

by Dr4gon39, Jan 26, 2017, 7:44 PM

This is bad

Rambling

by Dr4gon39, Jun 25, 2016, 12:55 AM

Sorry. Ive been rambling in the past few posts.

But, this is my blog. Its literally titled "My blog. Duh."

I do what I want.

*Evil sociopathic glint in eyes*
*Strange, sociopathic, Sherlock-esque smile*

On Summer and Boredom.

by Dr4gon39, Jun 25, 2016, 12:53 AM

I'm really bored, if you guys can't tell.

And I'll let y'all in on a little secret...I kind of don't really like summer.

Why?

Well starters, i get really bored. Basically I'll I've done the past few days are math and basketball. I know i'll be going to camp soon, but camp bores me too. Everything is slow, boring, sluggish, slow, slow, slow, and slow in the summer. And it kills me. Every single year.

Next reason....
School is fun. At least for me. I like school. Sure, school is stressful, I get that some people really really need a break from all that stress. And I get stressed during school too sometimes. I get it. But I'm the type of person who needs to be occupied, so I don't get so freaking boredddddddddddddddddd. And sometimes homework and tests are a pretty good way to keep me occupied. Also theres the plus side of there being math competitions during the school year. Ya know what I mean guys?

Next reason......
People. Yeah. That might come as a surprise. Some call me anti-social. Some call me socially awkward. Some call me bad with people. But in the end, I need people. Heck, I admit it. I do. I really do need people. And I um, really only have good friends in school. And I don't really see these friends in the summer. Thus, boredom. And like, these people that Im friends with, they're kind of good people, at least if you ask me. And, um, I might even miss some of them ( I know right, Dr4gon39 missing people???? Impossible.) But I do. And that sucks. Ergo, Summer sucks. It really does.

Some people countdown to schools end.
I countdown to its start.

Down with the tyranny of summer!
Down with the tyranny of ennui!

Ugh Im really bored I'm making blog postssssss

ugh boredom.

But yeah. Down with summer. Down with boredom.

Long live school.

summer

Boredom

Musings

Boredommmmmmmm

Why did I write the post below?

by Dr4gon39, Jun 25, 2016, 12:44 AM

I'm bored. Its summer.

On Hamilton and History

by Dr4gon39, Jun 25, 2016, 12:44 AM

So besides math the other subject that I like the most is definitely history...

In fact I probably like school history at least a teensy more than school math....

Competition math definitely better than school history though....

But anyways, Hamilton is really really cool. Really.

I know that some people don't get it, like, why would you want to listen to someone rap about a bastard, orphan, son of a whore and a scotsman.., while you could like, listen to eminem throw lyrics at you at supersonic speed. But anyways, Hamilton appeals to me. A lot. I can't even pinpoint why. Perhaps its just my love for history. Dunno. But Hamilton is awesome and that is the point of this blog post. I recommend you all take the chance and listen to the entire album in the right order at least once, (thanks for recommending that to me, you know who you are *winks*).

And why do I like history?

I do know that... like... unlike Hamilton.... there is a specific reason to that.
So History is this interesting thing. It repeats itself. In fact, I even started all my 6th grade history essays with something that looked like "through the cycles of history", and my teacher (who I credit for making me love history) gobbled it all up. But yeah, history does repeat itself. It teaches us about what goes on now, and it teachers us where all the greats made mistakes. But most importantly, from all the mistakes the greats made, we learn from them. And because of that, we become better people.

Love Hamilton. Love History.

hamilton

history

American History

LMT (I know finally).

by Dr4gon39, Jun 25, 2016, 12:28 AM

So I'm really bored right now because you know, summer...

So I thought I'd finally post on LMT, as requested.

Forgive me y'all if my memory is kinda fuzzy.

LMT was my last ever middle school math competition.

So our school decided to send two teams, the A team consisting of Me, willwin4sure, dckx15, supermath7676 and redsoxfan. We also sent a B team but none of them really use AoPS so they're really quite irrelevant. I also tried to get cedric-the-reindeer to sign up but he/she didn't so whatever.

So we got there like, tooooooo early. We sat in the auditorium for a while and talked and took some pictures *cough* adults *cough*. Then our friends from flame math came and we made some small talk and whatnot. Then Clarke 1 came in, and they asked us where ghghghghghghghgh was. Benstien was there, but janabel (that's her username, I promise) wasn't because she was at like this orchestra thing. That's also why Doherty didn't send a team, so we didn't see OpalSeaDrag0n9 or ilikepie2003. But anyways it was kinda cool that Clarke 1 came to talk to us and flame math. (Sidenote on Clarke: Me and my friends have pretended that we're in a rivalry with Clarke ever since 6th grade, but in reality, we know we're rather insignificant in comparison to Jonas Clarke, so its kind of a quasi-pseudo-rivalry at most. But anyways, its been fun competing with you guys for the past three years, watching you guys blow us all away for the past three years. If you read this, best of luck in the future, and know that there's this little school in Andover vying to usurp your dominance one day (heheheheh just kidding, lets all be friends, am I right?))

But then the competition started, so we went into the testing room.

Individual round was hard. I think I only answered like 12 or 13 of the 20 (I think) questions.

But then came theme round.

Theme round was crazy...
One of the themes was about bijections, injections and surjections, and the explanation given wasn't exactly the best....
Also, all of the other problems seemed impossible too besides a few.... But yeah everyone did horribly on it.

Then came team round.
Me and willwin4sure went and did the proofs, but they were pretty hard. It was cool that I knew my proctor, because she did science bowl with ABCDE a few years back, but I promise there was no cheating. In the end we also worked on the potpourri with the other three guys, and we didn't do that good, but it wasn't that bad either. I just want to complain that they did put limits in the potpourri, but whatever, the problem wasn't hard.... Anyways, this group is usually pretty functional during team round.....

Then we had lunch. I had a lot of pizza. My friends know how much I eat. During lunch we all felt pretty terrible because we all thought that we did horribly during the rounds because all the questions were pretty hard, especially theme.... But anyways pizza was good.

Then came guts round. We got into the auditorium early, and me and dckx15 talked for a while with this LHS person who was running the competition about science bowl for a while which was pretty fun. Then we situated ourselves in the back of the auditorium and got ready for guts. The live scoreboard was pretty nerve racking. Of course, clarke 1 established a clear lead, and my team sort of floated around 3-6. Then we got down to the last two sets of problems and they shut down the scoreboard for "suspense reasons". The second to last set was extremely hard, because the problems were all related to each other, so we just put down 0 for all of them. Then we got to the last set, which was three estimation problems, that we did not get right.....

Then we waited for results.
I got 7th for individual round, which wasn't too bad (willwin4sure also got 8th). I got 10th for individual composite which wasn't bad at all considering my abysmal theme showing.... For team round we got 5th which also wasn't bad. Then guts round. OMIGOSH. We got 2nd. Crazy. Second Place. Just being Jonas. Which sort of makes it 1st place. Pretty cool if you ask me. Uhhhhh we also only got 9th for team score, which was slightly weird, but I guess its because half to eh team score is individual, so I guess some of our team members didn't perform up to standards on the individual rounds *hacking cough hacking cough*. But yeah the results weren't bad, especially with the 2nd place guts snag.

Overall, pretty good day if you ask me.

This post has been edited 1 time. Last edited by Dr4gon39, Jun 25, 2016, 12:31 AM

LMT

I failed

by Dr4gon39, May 23, 2016, 3:20 PM

Long story.

This post has been edited 1 time. Last edited by Dr4gon39, May 23, 2016, 3:21 PM

MBTI poll

by Dr4gon39, May 10, 2016, 1:01 AM

http://artofproblemsolving.com/community/c170h1240347_mbti_of_aopsers
If y'all loyal readers won't mind.

A proof that I came up with

by Dr4gon39, Apr 5, 2016, 1:09 PM

Given: $\frac{a}{b}<\frac{c}{b}$ , where $a,b,c,d$ are positive integers, and $\frac{a}{b}$ and $\frac{c}{d}$ are simplified fractions, prove that $\frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d}$ .

In order to prove that $\frac{a}{b}<\frac{a+c}{b+d}$ , we attempt to prove that their difference is positive.

We have:
$\frac{a+c}{b+d}-\frac{a}{b}$
$=\frac{b(a+c)-a(b+d)}{b(b+d)}$
$=\frac{ab+cb-ab-ad}{b(b+d)}$
$=\frac{bc-ad}{b(b+d)}$

Due to the fact that $b$ and $d$ are both positive, $b(b+d)$ must be positive, so now we are attempting to prove that:
$bc-ad>0$
Or in other words:
$bc>ad$

Suppose we have two positive fractions $\frac{x}{y}=\frac{w}{z}$
Then suppose we have another positive fraction, $\frac{e}{f}$
Then, $\frac{x}{y}<\frac{w}{z}+\frac{e}{f}$
We add the two fractions and we get,
$\frac{x}{y}<\frac{wf+ez}{zf}$
We now attempt to examine the relation between the product of the numerator of the first fraction and the denominator of the second fraction and the product of the denominator of the first fraction and the numerator of the second fraction.

We subtract the product of the numerator of the first fraction and the denominator of the second fraction from the product of the denominator of the first fraction and the numerator of the second fraction.

We have:
$y(wf+ez)-xzf=wyf+yez-xzf$
Since $\frac{x}{y}=\frac{w}{z}$
then $xz=wy$
Therefore, $wyf=xzf$
So:
$wyf+yez-xzf=yez$
Since $y,e,z$ are all positive numbers, then $yez$ must be postivie too.
Hence, the product of the numerator of the first fraction and the denominator of the second fraction is less than the product of the denominator of the first fraction and the numerator of the second fraction.

From this we can conclude:
if we have two fractions where $\frac{a}{c}<\frac{b}{d}$ then $ad<bc$

Back to the original proof:

We now know that the difference between $\frac{a+c}{b+d}$ and $\frac{a}{b}$ is positive, so $\frac{a+c}{b+d}>\frac{a}{b}$

Now, we must prove that $\frac{c}{d}>\frac{a+c}{b+d}$ .
We do this by subtracting these two terms.
We get:
$\frac{c}{d}-\frac{a+c}{b+d}$
$=\frac{c(b+d)-d(a+c)}{d(b+d)}$
$=\frac{cb+cd-da-dc}{d(b+d)}$
$=\frac{bc-ad}{d(b+d)}$
Since $b$ and $d$ are positive numbers, then the denominator is positive.
Since $bc>ad$ the numerator is positive.
Therefore the difference between $\frac{c}{d}$ and $\frac{a+c}{b+d}$ is positive.
Therefore $\frac{c}{d}>\frac{a+c}{b+d}$

From above we now have the inequality $\frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d}$ .

Thus, our proof is complete.

Application of the above statement:

MagMaR team round 2016 problem 15.

Find a fraction $\frac{m}{n}$ between $\frac{59}{80}$ and $\frac{45}{61}$ for which $n<200$ .

By the above statement, $\frac{59+45}{80+61}=\frac{104}{141}$ must be between those two fractions. Ergo, problem solved.

Credit:

Credit should be given to Mr. Li, one of my old math teachers for telling me about this statement.
I, myself first wrote this proof a year ago in Chinese.
A few days ago, after using this statement on MagMaR, I felt the urge to write a proof in English.

Disclaimer:

If this is an actual theorem/lemma, please tell me.
No copyright infringement or infringement upon intellectual property was intended.

If anyone has found more errors in my proof, please PM me, leave a comment, or give me a shout.

An easier proof written by RedSoxFan:

Part 1:

$\frac {a} {b} < \frac {c} {d}$

$ad < bc$

$ad+ab < bc+ab$

$a(b+d) < b(a+c)$

$\frac {a} {b} < \frac {a+c} {b+d}$

Part 2:

$\frac {a} {b} < \frac {c} {d}$

$ad < bc$

$ad + dc < bc + dc$

$d(a + c) < c(b + d)$

$\frac {a + c} {b + d} < \frac {c} {d}$

And we are done.

No copyright infringement or infringement upon intellectual property was intended

I'd just like to point out to all of the haters that I was the one who solved the MagMaR problem in 3 seconds, not the rest of y'all with these super simple proofs so.... Peace out guys *winks* *drops mic*

I'd also like to submit that RedSoxFan's proof is kind of just mine worked backwards and not as technical and thorough so.... *cues Taylor Swift voice* "haters gonna hate hate hate hate hate"

DISCLAIMER:

I in no way own the lyrics to Taylor Swift's song entitled "Shake it off", all rights to that song belong to her (or the company she's signed to or whatever)

Basically, I just don't want to get my pants sued off...

This post has been edited 13 times. Last edited by Dr4gon39, Apr 5, 2016, 11:24 PM

My MagMaR experience, as requested by willwin4sure

by Dr4gon39, Apr 4, 2016, 11:33 PM

OK so...
For those who don't know how MagMaR is formatted, there is an individual round, a wild round (also individual, but the speed requirement is two problems per minute), team round, and blitz round (similar to guts round).

And my team consisted of me, willwin4sure, Redsoxfan, ilikepie2003, and Emc2014

Our scores for individual round and wild round ranged from acceptable to mediocre, and our team round score was actually tied for second behind Flame Math (which had the legendary OpalSeaDrag0n9 and hghghghghghghg), with Jonas Clarke Middle A (Which have the legendary janabel and benstien and is all around legendary (anyone in the MA are will have heard about this team)). But then came lunch (in which we attempted to prove this statement: "If $a,b,c,d$ are positive integers, and $\frac{a}{c}<\frac{b}{d}$ where $\frac{a}{c}$ and $\frac{b}{d}$ are simplified fractions, then $\frac{a}{c}<\frac{a+b}{c+d}<\frac{c}{d}$ ), and then the blitz round. And allow me say, we bombed the blitz round. WE BOMBED THE BLITZ ROUND. The results were absolutely horrifying, and after that I really felt like smashing a chair (or a person for that matter). Then results came. So when they were announcing the team rankings, we got third. But then I was like "NO WAY!", scratch that. All of us (besides Emc2014 who had left before blitz (which means yes, we were technically one person short during blitz, thus giving us a slight disadvantage)), went like "NO WAY! IMPOSSIBLE!", but we still got up and were about to accept certificates. Expect it turned out they printed the wrong certificates (although I will cut them some slack seeing that they were just some MIT students running a live tournament for the first time ever). So then I was like "they must have calculated the score wrong or something, because third place isn't us". And combined with our past statements about the impossibility of us being third, the admins "recalculated" the scores, and it turns out that we were not third place, or not anywhere in the top five. SOOOOOO we were like...OK THEN, THANKS FOR GETTING OUR SPIRITS UP. So I was kinda depressed when I got home and whatnot.

MAJOR PLOT TWIST:
So we were still kind of in disbelief that we hadn't placed in the overall team rankings, seeing that my team isn't thaaaaaat bad. So our coach emailed for another "recalculation" and it turns out that they just printed the wrong certificates, so we were third place. HUZZAH! So in the end, we did hit our goal, seeing that we knew Flame math and Jonas Clarke were too legendary.
I feel waaaaaay better now.

The moral of the story?
Have faith in yourself.
(i.e. never let the admins of contests hear you doubt yourself)

This post has been edited 1 time. Last edited by Dr4gon39, Apr 5, 2016, 11:05 AM

Submit

ooh hello
by jj_ca888, Nov 18, 2019, 10:36 PM
it's been a good ride.
by ghghghghghghghgh, Jul 30, 2019, 2:17 AM
Vincent's Fan
by Supermath7676, Feb 14, 2017, 11:48 PM
Clearly just a function convolution.
by willwin4sure, Nov 28, 2016, 5:11 PM
yvincent
by ghghghghghghghgh, Nov 28, 2016, 1:22 AM
oh dearr..
by stephy2003, Oct 12, 2016, 4:55 PM
Lol @ghghghghghghgh when I delete your comment and the admins refer to it as taking out the "trash"
Touche
by Dr4gon39, Oct 11, 2016, 9:18 PM
Vincent's Fan
by Supermath7676, Oct 11, 2016, 8:13 PM
China......
by willwin4sure, Aug 4, 2016, 11:34 PM
all the many facets of me
by RedSoxFan, Jul 20, 2016, 10:21 PM
We need a chocolate bar
by stephy2003, Jun 23, 2016, 7:17 PM
Post on LMT?
by willwin4sure, Apr 20, 2016, 8:53 PM
King of kings. XD I thought you were the doctor of sides Dr. Gon.

@dckx because /Wilma/ didn't elaborate with instructions. I is creary veri clueless
by stephy2003, Apr 17, 2016, 3:27 AM
You lost your chance...
by dckx15, Apr 16, 2016, 9:24 PM
AHEM.
BEHOLD THE KING!
THE KING OF KINGS!
by Dr4gon39, Apr 16, 2016, 1:45 PM
~~He's coming back soon, do we want to kill his blog or not?~~
by stephy2003, Apr 15, 2016, 12:13 AM
You're very welcome
by willwin4sure, Apr 13, 2016, 9:22 PM
~~Thanks for knowing my name~~
by stephy2003, Apr 13, 2016, 2:07 PM
Stephen you can post right?
by willwin4sure, Apr 13, 2016, 12:23 PM
~~Guys his in D.C. this week, let's kill his blog~~
by stephy2003, Apr 12, 2016, 11:44 PM
Are you not going to talk about LMT?
by dckx15, Apr 11, 2016, 4:13 PM
Lolololol RedSoxFan just rekt your proof
by willwin4sure, Apr 5, 2016, 10:50 PM
Yay you fixed the typos
by RedSoxFan, Apr 5, 2016, 10:15 PM
@willwin4sure, i dunno, is that allowed?
by Dr4gon39, Apr 5, 2016, 8:44 PM
No Mr. Gon, willwin4sure is
by stephy2003, Apr 5, 2016, 8:14 PM
Can't you just cross multiply to determine if a/b > c/d then ad>bc?
by willwin4sure, Apr 5, 2016, 5:22 PM
You have too many typos
by RedSoxFan, Apr 5, 2016, 5:13 PM
#**********CLUBTAKEOVER.
Harvard is next.
by willwin4sure, Apr 5, 2016, 11:58 AM
I'm obnoxious?
by Dr4gon39, Apr 5, 2016, 11:03 AM
yes he was
and to me
and redsoxfan
by ilikepie2003, Apr 5, 2016, 12:46 AM
Were you obnoxious to Emc?
by stephy2003, Apr 5, 2016, 12:41 AM
Post about your amazing MagMar experience.
by willwin4sure, Apr 4, 2016, 10:10 PM
~~a phat lizard~~ someone who can post, but usually doesn't. I kind of just use it to bookmark blogs. amd this is why summitwei never gets any views from me
by stephy2003, Mar 16, 2016, 2:58 AM
Dunno. HWAT is a contrib?
by Dr4gon39, Mar 16, 2016, 2:31 AM
Can I be a contrib? Thx!
by ilikepie2003, Mar 4, 2016, 3:59 AM
Good luck on the AIME today!
by stephy2003, Mar 3, 2016, 11:05 PM
Well I guess the only thing different are the amount of h's in UGHHHHHH
by ilikepie2003, Feb 29, 2016, 12:12 AM
Agreed @stephy
by dckx15, Feb 28, 2016, 3:54 PM
Barely refrains from saying real name. *@Dr4gon39*, you have the most creative post names, I mean they totally aren't annoyingly repetitive
by stephy2003, Feb 24, 2016, 12:51 AM
ALLO
C'EST MOI
by ilikepie2003, Feb 20, 2016, 10:30 PM
Second Shout.
by stephy2003, Feb 19, 2016, 3:41 PM
first shout >
by doitsudoitsu, Feb 17, 2016, 12:17 AM

42 shouts