General

[quote=justin9er]u just reiterated what i said....
we are calculating twice the area with respect to two trees placed on a diagonal, which i did at the very end,

someone already solved it using geometry[/quote]
You're using the diameter of the trees :S

@Avatar: Pointless? :l

[quote=PaniniSandwich]@carbunion Wow great job <3

"at least TS is interested in the puzzles and has a taste for elegant solutions."
What do you mean by that ^?[/quote]

Lmao she just said the same thing but with more mathematical language which i was trying to avoid and save you the trouble. This thread is so pointless I can see why people don't even bother helping on basilmarket

@carbunion the most amazing one as in the most amazing answer?

[quote=carbunion]To his credit, at least TS is interested in the puzzles and has taste for elegant solutions.

Actually I just found another way to do it - which seems to involve fewer operations:

Let ABCD be the original park.
Intersect diagonals AC and BD at center P.
Draw four circles centered at the corners of the original park so that they go through P.
These four circles will all meet at P, there are also 4 other points they meet at.
Those are the corners of the new park.

TaDa![/quote]

Because if you can't walk in straight lines, you can totally create perfect circle. Get off your high horse the question is about being efficient not elegant.

[quote=justin9er]here we go:
we all know that area of a square is: A = (s)(s)
but it can also be written as A = 1/2(d1)(d2) where d1 and d2 are the diagonal* of the square (@BishopPanini Fixed That Word <--)
if you assume both trees have an equivalent diameter x, then we can say that the diagonal can be equal to the sum of the diameters of the trees, equal to 'D'
because it is a square, the diagonals are equivalent
therefore the original area 'A' = 1/2 (D)(D)
we want twice the area, therefore... A' = (D)(D)

so basically you are saying that if you assume a diameter of the tree 'd' , figure out how many trees it will take to stretch the diameter 'x' , then multiply them together and square it = (x^2)(d^2)[/quote]
Oh god </3 I'm only 12 its hard to understand all of this & these symbols & stuff >-<
I'm a dumb person, okay?

[quote=justin9er]here we go:
we all know that area of a square is: A = (s)(s)
but it can also be written as A = 1/2(d1)(d2) where d1 and d2 are the diagnals of the square
if you assume both trees have an equivalent diameter x, then we can say that the diagonal can be equal to the sum of the diameters of the trees, equal to 'D'
because it is a square, the diagonals are equivalent
therefore the original area 'A' = 1/2 (D)(D)
we want twice the area, therefore... A' = (D)(D)

so basically you are saying that if you assume a diameter of the tree 'd' , figure out how many trees it will take to stretch the diameter 'x' , then multiply them together and square it = (x^2)(d^2)[/quote]
Not sure what you were saying at the end there, but we know that d1 = d2 (square), so A = 1/2(d^2), which means for A' = 2A, A' = d^2, since A' = L*L, L = d.

@carbunion Wow great job <3
[quote=Carbunion]To his credit, at least TS is interested in the puzzles and has taste for elegant solutions.[/quote]
"at least TS is interested in the puzzles and has a taste for elegant solutions."
What do you mean by that ^?

The distance between the trees is the side length of your new park.

#1
2,9,4
7,5,3
6,1,8

[quote=PaniniSandwich]Nooo I mean like its takes up too much time... </3[/quote]

Sorry to break it you but that's as simple as it gets. Without any basis of measurement the only method is compass and straightedge geometry.... kids these days....

[quote=Avatar]Too much work? It is as simple as fractions in grade 5. Can you divide a square into 4 even parts? All you have to do is draw a diagonal through each of the smaller squares to make a diamond shape. That diamond shape has half the area of the first square you drew...[/quote]
Nooo I mean like its takes up too much time... </3

[quote=PaniniSandwich]@Avatar - That's too much work !~ [/quote]

Too much work? It is as simple as fractions in grade 5. Can you divide a square into 4 even parts? All you have to do is draw a diagonal through each of the smaller squares to make a diamond shape. That diamond shape has half the area of the first square you drew...

@Avatar - That's too much work !~

Easy. Walk across the diagonals and plant a marker at the corners of the orignals park. (Two corners are assumed.) Then create a new square that contain those points at its edges. picture regular square, Join the midpoints at each edge to create a smaller square thats tilted compared to the original. If you drew it correctly you have a big square split into 4 smaller squares and a new square that talks up half of each of the 4 squares. 4/2=2 and the bigt square was 4 squares so the tilted square is half the original area in area. Your doing this in reverse.

@PaniniSandwich: well you can also use your height. like im 5'5 so i can lay down and see how many of me it takes.
walking will take a while, depending how big the park is.
and kk!

[quote=mechibi]cant you use your thumbs as a form of measurement?[/quote]

I would agree with your first post to a point.
First you should make an assumption that all the trees are the same size (it may be unrealistic).
Have the trees go along a diagonal line from the old - old tree, this will give you a number of trees that can be used as a "base" area.
Add one tree to each side (of the old - old trees) until the total number of trees you have is double that of the "base",
Using said assumption would mean that the area is doubled.

@mechibi - You probably can
What I was thinking as using your foot as a measurement. Like walking foot in front of the other from the top left corner to the top right then doing the same from the top right to the bottom right & the doubling the size of the park like that. But I'm not sure. I'll ask tomorrow :l Message you then!~ Kay?
@justin9er - You don't have any measurement or square grid of the park.. That picture that's there was a reference I just made in paint. >->
The only type of measurement you have is your body. :l
@razormana - Can't add anything to the park.. Just increasing the area..
@mechibi - Yeah you can do that. But it will be hard to save where you ended up at, get up & repeat. :l

cant you use your thumbs as a form of measurement?

Saving my post. editing later

@mechibi - Added a link at the bottom
@BleuVolleur - You cannot use any measurement tools :l [quote=BleuVolleur]measuring the distance between the two trees, and double the distance[/quote]
+ there is not square units.. there is no gird for the park; its just a flat park.. :l

by how many trees it can fit?
for example, twice the area= twice the trees

uh can you draw this for me, visualizing would be easier