P. Erdos and R.L. Graham- On Packing Squares with Equal Squares

  • Upload
    mnaom

  • View
    25

  • Download
    0

Embed Size (px)

Citation preview

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~ ~ ~~ ~~ ~ ~~~~~~~ ~~~ ~~~~~~~ ~~ ~~~~~~~~~~ ~~~~ ~~ ~~ ~~~~~~~~~~~ ~~~~~~~~ ~~~~~ ~ ~~~ ~~~ ~ ~~~ ~~~ ~ ~ ~~~~~~~~~~~~~~ ~~~~~~~~~ ~ ~~~~~~~ ~~~ ~~~~~~~ ~~ ~ ~~~~~~~~~ ~ ~

~ ~~~ ~

~~ ~~ ~~~~~ ~~~~~ ~~~~~~~~~

~~~~~ ~~~ ~~~~~ ~ ~~~~~~~~~ ~~~~ ~ ~ ~ ~~ ~~ ~~~~~~~~~~ ~~~~~ ~~~~~~ ~ ~~~~~~ ~~~~~~~~~~~~~ ~ ~~ ~~~~~~~~~~~~ ~ ~~ ~~~~~ ~~ ~ ~ ~~~~ ~~ ~~ ~ ~~~~ ~~ ~~~~~~ ~~~~ ~~~~ ~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~ ~~~~~~~~~~ ~~~ ~ ~~~ ~ ~~~~~~~~ ~~ ~~~~ ~~~~ ~~ ~~ ~~~ ~~~~~~~ ~~~ ~ ~~~~~~

~ ~~~~ ~~~~~~~ ~ ~~~ ~ ~ ~~~~~ ~ ~ ~ ~~ ~~~~~~ ~~~~~~ ~ ~~~~~~ ~~~~~~ ~~ ~~~~~~~~~~~ ~~~ ~~~~~~~~~ ~~~~~~ ~~~ ~~~~~ ~~~~ ~~~ ~~ ~~ ~~~~ ~~~ ~ ~ ~~~ ~~ ~~~~ ~~~~~~~ ~~~~~~~~ ~~~~~ ~ ~ ~ ~~~~ ~~~~ ~~ ~~ ~

~~~ ~ ~~ ~~~~ ~~~ ~ ~~~~ ~ ~~~ ~~ ~ ~~~ ~~~~~ ~~ ~~~~~~~~~ ~~~ ~~

~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~ ~~~~~ ~~~~~~~ ~

~~~~~~~~ ~ ~~ ~~ ~~~~~ ~~ ~ ~~~~ ~ ~ ~~~ ~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~ ~~ ~~~~~~~~ ~ ~~~ ~~~ ~~~~~~~~~ ~~~ ~~~~~~~~~ ~~~~~~~~~~~~ ~~~ ~~ ~~ ~~~~~~~~~~~ ~~ ~~~~~ ~ ~~~~~ ~ ~ ~ ~ ~~~~~ ~~~~ ~ ~~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~ ~~ ~~~~~~ ~~~~ ~~~ ~ ~~~~~~~~ ~~~~~ ~~~~~~~~~ ~ ~~ ~ ~ ~~~ ~ ~~~~~~~~~~ ~ ~~~ ~~ ~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~ ~~~ ~~ ~~~~~~~ ~~~ ~~~~~~~~~~ ~~ ~ ~~~~~~~~ ~~ ~ ~~ ~~~~~~ ~ ~~ ~~~~~~~~~~~~~ ~~~~ ~ ~ ~~ ~ ~~~~~~ ~~ ~ ~~ ~~ ~ ~~~~~~ ~~~~~ ~~ ~~~ ~ ~~~~~~~~~ ~~~~ ~~~ ~~ ~~~~~~~~~ ~~~~~ ~ ~

~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~

~~ ~~~~~ ~~~~~~~~ ~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~ ~ ~~~ ~~ ~~~~~~ ~ ~~~~ ~ ~~ ~~~~~ ~~~~~ ~~~~~~~~~~ ~~~~~~~ ~~~~~~~~~~~ ~~~~ ~~~~

~~~ ~~~ ~ ~ ~~~~~ ~ ~~ ~ ~ ~~~~~~~~ ~~~~~~ ~~~~~~~ ~~~~~~~ ~~ ~~~~~ ~~ ~~ ~~~~ ~ ~~~~ ~~~~~~~~~~ ~~~ ~ ~

~~ ~ ~~~~ ~~~~~~~~~~ ~~~ ~~~~~ ~ ~~~~

~~~ ~~ ~~~~~~~~ ~~~~~~ ~~~~~~~~~~ ~ ~ ~ ~ ~~~~~ ~~~~ ~~~~~~~ ~~~~~~~~~~~ ~~~ ~~~~ ~~~~~~~~ ~ ~ ~~~~~ ~~ ~~ ~~~~ ~~ ~ ~~~~~~~~~~~~~~

~~~~ ~~~~~~~~ ~~

~~~ ~~~~~~~~~

~~ ~~ ~ ~~~ ~ ~ ~~~~~~~~~~~ ~ ~ ~~ ~~~

~~~~~~~~~~ ~~~~~~~~~~~ ~~ ~

~~~~~ ~~~~ ~~~~~~~ ~ ~ ~~~~~ ~

~ ~~ ~ ~~ ~ ~~~~~ ~~~~ ~~ ~ ~~~~~~ ~~~~~~~~ ~ ~~~~~~~ ~~~~~~~~~ ~ ~~~~~~ ~~~ ~~~~ ~~~~~~~~ ~ ~ ~~~~~ ~ ~ ~~~~~~~ ~~~ ~~~

~~~~~ ~~ ~~

~~~~ ~~~ ~~~ ~~~ ~~ ~

~~

~~~~ ~~~~ ~~~ ~ ~ ~ ~ ~~~~~~~~~~~ ~ ~~~~ ~ ~ ~~~~~ ~ ~~~~~~~~~ ~~ ~~ ~ ~ ~ ~~ ~ ~~~~~~~~ ~

~~~~~~~~~~~~~~~~~ ~ ~

~~ ~~~~~~~~ ~~~~ ~~~~~ ~~ ~~~~~~~ ~~~~~~~~ ~ ~ ~~~~~ ~~~ ~ ~~~~~~~~~ ~ ~ ~ ~~ ~ ~~ ~~~~~ ~~ ~ ~~~~~~~~ ~ ~~~~~~~ ~ ~~~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~ ~~~ ~

~~~~~ ~~~~~~~~~~~~~ ~ ~~~~~~~~~~ ~~ ~~~ ~ ~~ ~ ~~

~~~~~~~~~~~ ~~ ~~~ ~~ ~ ~ ~~

~

~~~~~~~~~~~~~~ ~~~ ~ ~~ ~~~~ ~~ ~~ ~ ~~~~~~~~~ ~ ~~~~~ ~ ~ ~ ~~~~ ~~~~~~~~~~ ~~~ ~~~~~~~~~~~ ~~~~~~ ~~~~~~~ ~~~~ ~ ~~ ~~~~~~ ~~~ ~~

~ ~~ ~~~~~~~ ~~~~~~~~~ ~ ~ ~~~ ~~~~ ~~~~~~~~ ~ ~ ~~~~~ ~~ ~~~~~ ~~~~~~~~ ~~~ ~~~~~~~ ~~~~ ~~ ~~ ~~~ ~~~~~ ~~ ~~~ ~~ ~ ~~~~~ ~~~~~ ~~~~~~~ ~ ~~~ ~~ ~~~ ~~ ~~~~~~~~~ ~~~~~ ~ ~~~ ~~ ~~ ~~~~~~~~~~ ~~~~~~~~~ ~ ~~~~ ~ ~~ ~~ ~~~~ ~~~ ~~~ ~~~~~~~ ~~~ ~~~~~~~~ ~~~~~ ~~~~ ~ ~~ ~~~~~~ ~~~~~~ ~~~ ~ ~~~~~ ~ ~~~~~~~ ~~~~~~ ~ ~~~~~~~ ~~~~~~~ ~~~~~~~~~~~ ~~~~ ~~~~

~~~ ~~~~~~~~ ~~ ~~ ~~~~~~~~~~~~~ ~~~~~~~~~ ~~ ~~~~~~~ ~ ~ ~~~~~ ~~~~~~ ~ ~~~~~~ ~~~ ~~~~~ ~~ ~~~~~~~ ~ ~~ ~~~~~~~~~ ~~~~~~~~ ~~~ ~ ~ ~~~~~ ~~ ~ ~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~ ~~~~~~~~~~~ ~~ ~~~~~~~~~ ~~ ~~~~~~~~~ ~~~ ~~ ~~~~~~~~~ ~

~~ ~~ ~~~~~~~~~~~~

~~ ~~~