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Variables: Big Squares and SmallSquares

You might want the turtle to draw squares withsides of 60,50,100,10 and so on. One way of doingthis is to have many procedures: s q u a r e 100,

s q u a r e 50, s q u a r e 33, etc. But there must be abetter way, some kind of shortcut; and, of course,there is. We can change s q u a r e s o that it is likef o r w a r d in that it takes an input. Then we cantell s q u a r e how long to make its sides by typing

SQUARE 50

SQUARE 40SQUARE 30

So lets make a procedure for drawing variablesized squares, b o x might be a suitable name sinceit reminds us of squares. But well meet a newidea by calling it b o x r (usually pronounced likebox-are) which makes us think of a right-turningsquare. We could also define a left-turning boxand call it b o x l (usually pronounced box-ell).A shortcut method for typing in the definition ofb o x r is to modify s q u a r e in the editor. If wechange the name of the procedure before we leavethe editor we will not change the definition ofSQUARE.

EDIT " SQUARE

Now the Logo editor shows this procedure withthe! (cursor) on the t oft o .

TO SQUARE

FD 30

RT 90

FD 30RT 90

FD 30

RT 90

FD 30

RT 90

END

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First lets change the name of the procedure froms q u a r e to b o x r . The I (cursor) is sitting on the t of t o . Move it to the space after s q u a r e . Usec t r l -e .

TO SQUARE

Now erase the word s q u a r e using the - key andtype the word b o x r

TO BOXR

Type c t r l - c . Logo respondsBOXR DEFINED

At this point b o x r and s q u a r e have the samedefinition. Now we change b o x r Type

E D I T " B O X R

The Logo editor now shows

TO BOXR

FD 30

RT 90

FD 30

RT 90

FD 30

RT 90FD 30

RT 90

END

We change b o x r so that it requires an input likef o r w a r d does. The procedure will be able todraw squares of various sizes. How do we tellLogo to do this?

The first instruction has to be f o r w a r d someamount, but when we are writing the procedurewe dont know what amount it will be. We handlethis situation by giving the amount a name. Forexample, lets call it s i d e . If we choose this name,

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we write f d :s i d e to mean f d whatever numberhappens to be called s i d e . So we can write

FDRT

FD

RT

FD

RT

FD

RT

: SIDE90

: SI DE90

: SI DE90

: SI DE90

One more idea is needed to turn this into a proce

dure. When we use the command b o x r we willnow have to follow it with an input like this:

BOXR

BOXR

20100

To indicate that b o x r needs an input and thatthis input will be called s i d e we do the whole pro

cedure like this:

TO BOXR : SIDE FD : SIDE RT 90

FD : SI DERT 90

FD : SI DERT 90

FD : SIDE RT 90

END

b o x r makes the turtle draw a square of any sizedepending upon the number you give it as aninput.

BOXR 10

BOXR 20

BOXR 30

BOXR 40 83

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We have just used a powerful mathematical idea the idea of variable. But instead of using a mys

terious x for the variable as we did in school alge

bra, we have used a meaningful name, s i d e .

When you were defining this procedure you wanted to tell the turtle how to draw a square, butyou did not know what size square you mightneed. Indeed, you wanted to be able to drawsquares of all possible sizes. When you came to typing the f o r w a r d command you knew thatf o r w a r d needed an input. You couldnt just typef o r w a r d without an input. You had to type f o r

w a r d something. To give this something a name,we called it s i d e . In Logo the expression :s i d e means whatever happens to be in the containercalled s i d e . If Logo is to carry out the commandf o r w a r d :s i d e there must be something in thecontainer.

The container is filled when you use b o x r andtype b o x r 10 or b o x r 15. When Logo obeys thatcommand, 10, 15, or whatever you typed as the input is put in the container named s i d e , b o x r can then look in the container at a later time.

Bug BoxPossible bugs:

1. You typed :SISE or some other spelling differ

ent from the way the input on the title line wetsspelled.

2. You forgot to use dots (:).

3. You inserted an extra instruction in b o x r .

4. You accidentally erased an instruction inBOXR.

5. You typed a space between : and s i d e .

6. You typed a : in front of a number.

--

----------------------------------------

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The character, : (dots), informs Logo that theword to which it is prefixed names a containerwhich can have in it a number, another word, a listof words, or a list of lists.

Some Uses ofb o x r

TO SQUARES

BOXR 10

BOXR 20

BOXR 30

BOXR 40

END

TO DIAMONDSRT 45REPEAT 4 [SQUARES RT 90]

END

TO FLAGR : S I ZE

FD : S I ZE

BOXR : S I ZE

BK : S I Z E

END

TO 6FLAG : S I ZEREPE AT 6 [FL AGR : S I Z E RT 60]

END

TO S P I N F L A G : S I Z E

6 F L A G : S I Z E

6 F LA G : S I Z E - 20

END

Being able to control the size of a shape makesthat procedure much more useful and interesting.

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I k 3 8 R T 1 2 0 3

Big Triangles and Small Triangles

We can also define a triangle procedure which

takes an input. Type

ED "TRIANGLE

Now the Logo editor shows this procedure with

the I (cursor) on the t oft o .

TO TRIANGLE

RE PE AT 3 [FD 30 RT 120]

END

Then change t r i a n g l e .

TO T R I A N G L E R : S I D E

REPE AT 3 [ F D : S ID E RT 120 ]

END

Use the procedure to make designs like:

TRIANGLES TRISTAR TREES

TRIANGLES

T O T R I A N G L E S

T R I A N G L E R 1 0

T R I A N G L E R 2 0T R I A N G L E R 3 0

T R I A N G L E R 4 0

END

TO TR ISTAR

R E P E A T 1 0 [ T R I A N G L E S RT 3 6 ]

END

TO TREE : S ID ERT 3 0 T R I A N G L E R : S I D E

RT 60 FD : S I DE / 2

LT 90 BK : S I DE / 2

END

TREES 86

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TO TREESTREE 30

TREE 40

TREE 50

END

Arithmetic

As you have learned from the examples above,you can do arithmetic in Logo. For example,

PR 5 + 3

Logo types8

PR 4 * 23

Logo types92

PR 345 - 32

Logo types3 13

PR 25 / 5

Logo types

5 .

Logo Numbers

Notice that the result of 25 divided by 5 is a deci

mal number. Logo has both decimal and integernumbers. Logo will perform arithmetic with deci

mals or integers.

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Some computations always result in a decimal an

swer. Division (/) is one of those. Other arithmeticoperations depend on what they are given as inputs. For example, if you type

PR 4 * 2 . 3

Logo types9 . 2

For more discussion about arithmetic in Logoconsult theReference Manual.

Logo Vocabulary

The character: (dots) informs Logo that the wordto which it is prefixed names a container whichcan contain a number, another word, a list ofwords, or a list of lists.

Arithmetic Operations

+*

88