Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2012-02-11 02:52:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

@MIF , Activity:Drawing squares

What's the formula for the number of those squares???

Last edited by anonimnystefy (2012-02-11 03:22:18)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#2 2012-02-11 06:29:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Hi anonimnystefy;

Could you tell me the link please?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#3 2012-02-11 06:39:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

it's on MIF page.

Activity:Drawing Squares

Last edited by anonimnystefy (2012-02-11 06:40:27)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#4 2012-02-11 06:45:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Hi;

Did you construct a table of the small values by hand?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#5 2012-02-11 07:10:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

nope.imma gonna.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#6 2012-02-11 08:46:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

here?

i have found that subtracting the 4th difference of the numbers gives 2,2,2,2,...

so we have: a_n=An^4+Bn^3+Cn^2+Dn+E.we can easily find those but what has actually been bothering me is the same tak but only on an m x n grid.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#7 2012-02-11 08:52:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Whoa! How about letting me see you sequence first? The one you got empirically.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#8 2012-02-11 08:55:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

n |a_n
--------
1 | 0
2 | 1
3 | 6
4 | 20
5 | 50
6 | 105


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#9 2012-02-11 08:56:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Now you actually did those by hand? Drawing tiny little squares until your fingers bled.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#10 2012-02-11 08:59:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

didn't do it for 6,but after finding the 3rd differences i saw that they were all squares.but i can easily check for 6. tongue


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#11 2012-02-11 09:01:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

First things first. I notice your sequence is shifted. You can adjust that.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#12 2012-02-11 09:06:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

i used 1x1 grid to be just a dot.seemed more logical.
2x2 was this:
.  .
.  .


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#13 2012-02-11 09:10:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Hmmmm, but the problem as outlined uses the convention of counting interior squares and not lattice points. Since we are counting squares do you not now think that it is more consistent to set the problem up in terms of squares?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#14 2012-02-11 09:12:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

ok,then just shift the whole sequence by one to the left.

Last edited by anonimnystefy (2012-02-11 09:12:47)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#15 2012-02-11 09:14:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Kayrect! Now what would you do to go about getting a formula, remember to shift your list first.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#16 2012-02-11 09:44:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

???


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#17 2012-02-11 09:46:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

so we have: a_n=An^4+Bn^3+Cn^2+Dn+E.we can easily find those

From here.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#18 2012-02-11 10:10:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

but it's better to expand that.get a better form for working with it.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#19 2012-02-11 10:13:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Maybe, but that form makes you look like a combinatorial genius. People will be in awe of you.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#20 2012-02-11 10:15:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

maybe,but i know that you're a combinatorial genius,so you don't have to prove it. big_smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#21 2012-02-11 10:20:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

When I was 4 I was rated with the IQ of a genius. But now that I am 9, I am rated as an imbecile.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#22 2012-02-11 10:47:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

i'm happy for you.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#23 2012-02-11 13:46:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

Thanks, I am happy for me too. Now people come by and pat me on the head and tell me there will someday be a cure.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#24 2012-02-12 04:11:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: @MIF , Activity:Drawing squares

what about an mxn grid,i.e a rectangular grid?

Last edited by anonimnystefy (2012-02-12 04:11:14)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#25 2012-02-12 04:24:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: @MIF , Activity:Drawing squares

For that I have:

I do not know if it is correct. Perhaps you would like to test it?

Break time! Pass me the pancakes!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB