Last Blog Entry

Hi folks,

It was a wonderful class overall. You may be young in years but not young in the deeper sense and there is so much life and adventure waiting for you to be unfolded and created. I created this last post for you to share ideas and who know, maybe it will not be the last.... but the river of life goes on my dear friends and the stream is strong and swift...

Much Love,

--Dani

Final Project Groups

Here are the groups for the final project. These groups should also make there Monday Math Fair in Emerson presentation together as well. INjoy!!! (yes i mean "IN"joy)

1. Vincent, Bekah
2. Joshua
3. Jason, Amanda, Amiee
4. Crissie, Joe, Jahna
5. Frank, Jon
6. Junior, Colleen, Megan
7. Steve
8. Kelly
9. Tati, Kristy, Maureen

Ideas for final project

Use this post to share ideas: This is what i wrote:

Folks,

I wanted to remind you that I created lots of help for you on seelogo.

Simply go to lessons and click on Math Art.

Both for the previous stuff and dynamic Art. I know you will apprecaite it and enjoy playing with it.

Here is also another suggestion for groups to play with (some more technical people can help with the computer and others with suggestions etc.)

I click on the abc button, chose a color and wrote the text" My first Semester: it it came in big black letter on the screen. I then tyoe Flash 0.1 It (thanks to David and Josh!!)

What you saw in the "left brain" that is the editor was something like:
flash 0.1 [COLOR BLUE[GT -143 26 STRETCH 127% [SIZE 240% [WR "My first Semester" ]]]

Now comes the fun part:

Every number you see in this program can become a variable and even the words themselves "My first Semester" can change.

Remember that 127% = 1.27 etc.

so if you change this programs to something
local t x y s etc
loop 100000 [t=t+1/100000 x=___ y=____ s=____ etc..
flash 0.1 [color blue [GT x y STRETCH s [SIZE 240% [WR "My first Semester" ]]
]]

If you play with different functions you can make amazing things happen.

You can also change the colors instead of blue write RGB c1 c2 c3 where c1 c2 c3 are functions...

--Dani

Final Project Update

FINAL EXAM:
Easy, Med, Thought Provoking. For each please submit to the appropriate folder located on the Q: drive (i.e. easy) a seelogo demonstration and a .doc (Microsoft word document) explaining the seelogo demonstration.

Easy: Due Nov. 29

Medium: Due Dec. 4

Thought Provoking: Due Dec. 6

JOURNALS:
Journals (that everybody kept up with, right?): Due Dec. 6


MATH PRESENTATION (EMERSON):
Enhance your "Thought Provoking" from what you feel in your soul You do not have to hand in a word document explaining what it means. It's like real life, you have to be able to back up what you say, but there are always things that sometimes we just don't understand'.

Presentation: Dec 10th

FINAL PAPER:
Suggested Guidelines for paper:
1. Experience as a freshman
2. About the course (Seelogo)
3. Reflection
*. Pros & Cons about the course, suggestions for improvement...

Paper: Due December 18th @ 10:30am (final project time)

FINAL EXAM TIME:
There is a forum planned with pizza and good times. You may bring your paper to talk about your experiences as a 1st year at Ithaca College.

December 18th @ 10:30am

final project

FINAL PROJECT!!!!!!!!!!!!!!!!!!!!!!!!!

Easy: Due Nov. 29

Medium: Due Dec. 4

Thought Provoking =0 : Due Dec. 6

Journals (that everybody kept up with, right?): Due Dec. 6

Presentation: Dec 10th

Final Paper: Due Dec. 13
Guidelines for paper:
1. Experience as a freshman
2. About the course (Seelogo)
3. Reflection

Practice for test for next week (Thursday)

Here are some questions that you may want to practice. The only HW this weekend is to complete the assignment and practice for the test.

The best way to learn is to try to do it on your own. When needed look at the solution (first comment) and then try again. Write notes. Once you get it do not stop there. Come back to it later and do it again until you start feeling really good inside. It will be such an enjoyable experience at the end. :)

1. Can you explain in your own words the meaning of the commands and why do we need themm:
A. local t x y etc.
B. t=t+1/10000
C. loop
D. x=100*t jt x x
E. r=circle 100*t


2. Make a small program w/o looking ta any notes that moves a small circle from:

A. (0,0) to (100,0)
B. (20,100) to (80,100) How would you slow it down by a factor of 3?
C. (100,100) to (0,0)
D. (15,60) to (-120, 110) How would you make sure the answer is correct?
I suggest to practice with D a lot by picking up your own points and testing yourself.

3. Make a small program that moves a small object chaning colors randomly around a circle of radius 120 5 times around the center of the screen
////////////////////////////////////
If master this up to here you are a B student on this material. If you want go further.

4. Modify the previous program so that it creates a spiral rather than a circle and turns around the center 3 times

5. Make a program that moves two points at the same time from (100,100) and (-100,-100) and meet at the origin and then make the spiral of life explode

6. Make a program that moves a point from (0,0) to (100,0) and then from (100,0) to (100,100)

7. Move an object along a line segment hence and forth 5 times <------------>

8. Play with colors that change smoothly and not randomly

Labyrinth design

Please try to decipher the code in the picture so that will match the actual Labyrinth that can be found in:

http://pvs.k12.nm.us/OutdoorPages/labyrinth/labyrinth-design-6.jpg


The puzzle is to find the connection between the code at the top of the picture and the actual picture.

deepening understanding of functions

Using SeeLogo to Understand Functions

We can use SeeLogo to create a picture that changes in time. One good reason to do this is so that we can become familiar with using functions and manipulate them to achieve certain desired effects.

In order to carry out this exercise, we need to translate our regular mathematical notation to the language that the SeeLogo program can understand.

Before we do this, let's review what a function is.

A function y=f(x) can be seen as a rule or a formula so that for every number x that we choose to use as input for the formula (and there may be some limitations), we are going to get another number y=f(x) that is called the output. To put it in words, we say, "y equals f of x," or "y is a function of x."

For many students, this seems strange at the beginning, but note that in spoken language, we also use this concept. For example, when we say, "His success in this endeavor depends on how much effort he put into it," or in short: "Success is a function of effort." Furthermore, we can say, "The temperature is a function of time; at night it is usually colder."

We also refer to the input (x in this case) as the "independent variable" and the output as the "dependent variable."

The choice of f x and y to express the function and its input and output is based on tradition and is not really essential. In fact, any symbol, letter, or word can be used. For instance, we could write r=g(t) to or salary=fun(seniority) or x=h(y).

Every function has a domain and a range. The domain of a function is the set of input numbers and the range is the set of output numbers. When we specify a function, we usually have to specify the domain as well, but the range is then determined by the domain.

In algebra and calculus, we use formulas to express functions and one of the simplest examples is y=x^2. If we specify the domain to be all the numbers x between 0 and 2 (0<=x<=2), then the range will turn out to be all the numbers between 0 and 4 (0<=y<=4).

When defining a function in SeeLogo, we usually want to use it to display pictures that change in time . In many situations we choose the symbol t (indicating time) to represent the independent variable. The dependent variable will vary and in most situations we will deal with several functions all of which will be using the same independent variable t. We will use these functions to "do things" graphically. For convenience we also choose the domain of t to be the interval between 0 and 1 (0<=t<=1).
Before going any further, let us study how to relate this information to the current version of SeeLogo.

When we define and use functions with SeeLogo, we need to start by defining a task. A function should have a function :). In other words, it should be functional and do something. For example:

Task: Draw a small circle that moves at a constant speed from the coordinate xmin=20 to xmax=100 where the vertical position is 50 pixels above the x axis.

In order to implement this function we first translate the task to succinct mathematical language:

Move a small circle at a constant rate from the point (20,50) to the point (100,50).

In this case we need to define just two variables: The independent variable with domain 0<=t<=1 and the function x=x(t) with range (20<=x<=100). There are two stages in creating the animation:

1. Finding the function x(t) and
2. Implementing it in seelogo.

The answer to stage 1 is:
The function x(t) = 20 + 80*t. The reason is that for t=0 x is 20 and for t=1 x is 100

The way we will program the computer to do this is (our first attempt is to explain it in human language

1.Define the variables t and x and set t=0
Local x t
t=0
2.Next repeat the following process 10000 time (Loop 10000 then open "["and close "]" at the end of the process
Add a small time increment to define a new time (t=t+1/10000)
Define the new value of x(t) (x=20 + 80*t)
Make the cursor (or turtle) jump to the new coordinate
Draw a small circle (circle 3)


The actual seelogo implementation is:
local x t
t=0
loop 10000 [
t=t+1/10000
x=20 + 80*t
JT x 50
circle 3
]

Now we will ask a series of question that will test your understanding and teach you further. Some of the questions are multiple choice:
1. Imagine that you type the following program into seelogo

local t x y
t=0
loop 1000 [t=t+0.001 x=100*t y=50*t]

A. what are the names of the functions involved?
1. x 2. y 3. t 4. x and t 5. x and y

B. What is the domain of the functions? ([a,b] means "all the numbers in between a and b"
1. [0,2] 2. [0,1] 3. [1,2] 4. [1,0]

C. What is the range of the function x?
1. [20,100] 2. [0,50] 3. [0,100] 4. [100,0

D. What is the range of the function y.

E. How will you slow the program by a factor of 100?

2. Write an increasing linear function with name x and domain t from 0 to 1 where x ranges from 50 to 120 (a function is called increasing if the output numbers become bigger as the input numbers increase)

A. x=50 + 70*t B. x=70+50*t C. x=120 D. x=120 - 70*t

3. Write an decreasing linear function with name x and domain t from 0 to 1 where x ranges from 50 to 120 (a function is called decreasing if the output numbers become smaller as the input numbers increase)

A. x=50 + 70*t B. x=70 - 50*t C. x=80 D. x=120 - 70*t

4. Find two linear function x and y so that x with domain t, 0<=t<=1 such that x starts at -100 and ends at 100 and y starts at 90 and ends at 10.
A. x=-100 + 200*t y= 10 + 80*t B. x=-100 + 100*t y=90 - 80*t C. x=-100 + 200*t y = 90 - 80*t

5. Write a small program that makes a small circle move from the point (-100,100) to (90,10)

local t x y
t=0
loop 100000 [t=t+1/100000 x=____ y=_____ JT __ __ ______ 3]
What are the blanks?

6. Now write a program from scratch w/o looking that does the same thing and test it
7. Write a program without looking that makes a small circle move from (120,-100) to (-110,90)

8. A. Find a function x with domain [0,1] and range [-100,100] and another function r with the same domain but range [0,100]
B. Write a program that uses the functions x and r so that a circle of diameter r is placed at the point (x,0).
C, change the program so that the color of the circle will be random.

Week 10/29 activities

This week we will devote time to plan the Math day on parents weekend and also learn about function and using them to change colors.


Below is a small program that I wrote which is based on the following principle


The Sin ranges from -1 to 1 and the RGB colors take input from 0 to 255 so:
In order to use the SIN function with colors we first need to make it positive (by squaring it) and next we multiply it by 255.



We will
local c1 x y s
t=0
loop 100000 [t=t+0.00001
c1=255*(Sin(360*3*t))^2
x=100*t y=100*t
jt x y color rgb c1 c1 c1 [circle 20]
x=-100*t y=100*t
jt x y color rgb c1 c1 c1 [circle 20]
]

Class discussions:

1. What does x=100*t y=100*t do in the program?
2. using more traditional mathematical notation from algebra and calculus. What is the equation
of the two lines.
3. What would you do in the program to add two more lines that will create a dynamic symmetry (everything will look "perfect" and happen at the same time)
4. How would you change the program so that the movement will happen along parabolas (say with an equation like y=x^2 etc...
5. In what other ways can you change colors. Let us discuss it and implement it.
6. What other functions do we know? How to implement them? What other curves can we think about and how can we implement them
7. In what other ways can we change colors creatively?
8. How can we change the sizes of shapes we are doing.

HW for next two weeks:
1. for next week: Summarize in this blog the answers to these questions in your own way and share some ideas and techniques. help others. they will appreciate your creativity.
2. For next week. Come to the Math day even for just a few minutes. If you can help more
3. Two weeks for today. Create your first major math art piece to show to the class and try to add music also. It will be asam (sp?). The name of the directory to save your work is Project_11_11_07

Walking the Labyrinth.

The labyrinth is a sacred mathematical and spiritual path that allows one to connect with their soul. Our classes will build the Labyrinth today (10/22/07) and each one of us either alone or with a friend will walk it sometime before 11:00 tomorrow morning (10/23/07). Please use this blog to record and share your experience.

Week 8: Introduction to Function HW Due 10/29

1. Review Introduction to Function Unit and practice the examples there.

2. The following program draws a graph function
local x y
t=0
loop 10000 [t=t+0.0001 x=150*t y=70*Sin(4*360*t) jt x 0
FD y]

A. What is the period of the graph?

B. How would you slow the program by a factor of 10? What will you change? This means the program will run 10 times slower.

C. Why do we need the commands x=150*t jt x 0 in the program?

D. What does the number 150 control in the program?

E. What will you change in the program so that it will not fill in the area but just draw the graph of the function itself? Hint: Instead of FD y try GOFD y or JT x y

F. What will you change in the program to make it draw a circle of diameter 100 with random colors ranging from 0 to 511

G. What will you change in the program to make it draw a spiral with random colors

H. Create a suprize piece of Mathematical Art and paste to code in your answer.

Week 8: Introduction to functions

We will introduce this post to fun functions in SeeLogo and the result will be beautiful presentation for our December 10 Exhibition:

We start the session by declaring the global time variable t
(type declare t)

Our first function is P1:
New P1
jt 0 100
t=0
loop 10 [t=t+0.1 wrnum t]

The result is that 10 numbers from 0.1 to 1 will be displayed. For convenience we will always have the time t change from 0 to 1.

---

The next program is similar except that now 1000 numbers are displayed. This will allow smoother projections of movements on the screen that will be more pleasing to the senses.

New P1A
jt 0 100
t=0
loop 1000 [t=t+0.001 wrnum t]
jt -100 0
wrnum t

//Notice that t=t+0.001. This is not an accident since we ask that t is between 0 and 1.

---

The Next Program defines a function y where y=100*t (similar to y=100*x that you may be more familiar with)

New P2
local y
t=0
loop 1000 [t=t+0.001 y=100*t wrnum y]
JT -100 0
wrnum t
wrnum y

---

Next function is based on the Sin(x) function which you may heard about. We will explain it in detail in class: The actual function here is y=40*Sin(360*t) and it has a single period. This may seems strange at first but after a while will make sense.
NEW P3
local y
t=0
loop 100 [t=t+0.01 y=40*Sin(360*t)
fd y bk y gomv 1 0 wait 0.1]

---

The next program is just like the previous one but with 3 periods.
NEW P3A
local y
t=0
loop 100 [t=t+0.01 y=40*Sin(3*360*t)
fd y bk y gomv 1 0 wait 0.1]

---

The next program uses the definition of the Sin and Cos Functions to make a colored circle
NEW P3B
local x y
t=0
loop 100000 [t=t+0.00001
x=100*Cos(360*t)
y=100*Sin(360*t)
jt x y color rnd 512 [circle 8]]

---

The next two programs show what rich potential we have here. Next week we will learn about functions and colors. Once you start mastering the technique you become a Mathematical artist. Please be patient. It takes some time to get used to the new concepts but they are not difficult.

NEW P3C
local x y d
t=0
loop 100000 [t=t+0.00001
d=30*(Sin(360*3*t))^2
x=100*Cos(360*t)
y=100*Sin(360*t)
jt x y color rnd 511 [circle d]]

New P3D
local x y d r
t=0
loop 100000 [t=t+0.00001
d=30*(Sin(360*2*t))^2
r=60*(Sin(360*2*t))
x=r*Cos(360*t)
y=r*Sin(360*t)
jt x y color rnd 511 [circle d]]

The Dalai Lama Visit

Please write what you learned and experienced from the Dalai Lama visit in Ithaca. Any thoughts?

Review problems and answers for test

I use this post to help you review for the test. You do not need to answer unless you want to.

The first comment has answers to the first set of questions and this link has review questions that we will go over on Thursday:

http://www.ithaca.edu/dani/classes/Mart/picture_puzzles/pictures_review/

Based on popular demand we added more pictures to play with. Have fun.... The first picture with the Ying and Yang is different then the rest and is like the flowers picture.

http://www.ithaca.edu/dani/classes/Mart/picture_puzzles/pictures_fun/

I was just sitting down to test out those SeeLogo pictures. I have gone through all of them already. They are very fun and relaxing to do in between doing homework. I was wondering if you could post more pictures on the blog as I am sure people will have gone through the ones already posted soon. I just think they are fun to think about and try to make so they don't have to be posted for just review purposes but for fun purposes! :)

Answer to 9/30 (flowers) problem

Here are the answers to the 9/30/07 flowers problem

When we look at all three pictures we start seeing something in common. Look at them. Do you see that the second picture actually contains the first one and that the this picture actually contains the second? Look at them and see that this is true. This is the idea behind a "fractal": A mathematical object that contains itself within itself within itself....forever.

So how can we create this idea in SeeLogo? First let us prepare three names that will define the three pictures and we can call them A1 A2 and A3.
so we can type:
NEW A1
NEW A2
NEW A3

right now A1 A2 and A3 are empty. They have nothing in them but in few minutes we will fill in the void.

The first picture (A1) consists of a line and a circle "spun 6 times around the center"
step 1: Make a line and a circle


In the SeeLogo language there can be many ways to do it. (Click on A1 first)

For example we could type in the command line:
GOFD 40 FD 30 CIRCLE 60
JT 0 0
SPIN 6 IT

Or type directly in the editor:
SPIN 6 [FD 40 GOFD 30 CIRCLE 60 JT 0 0]
--------------------

The 2nd picture will be A2.
The idea now will be to do to steps almost like before:

Step 1: Make a line and a circle and fir A1 inside the circle using proportion.
Step 2: Bring the point back to the center and spin the picture 6 times.

We note that in order to fir the also picture A1 into the small circle we need to scale A1 to fit in it. Since the Diameter of the big picture A1 is 2*(40+60)=200 and the diameter of the small circle is 60 pixels, the scaling factor is exactly 60/200=30%

To make it in Seelogo we click on A2 we click on A2 first and then type:

FD 40 GOFD 30 CIRCLE 60 SIZE 60/200 [A1]
JT 0 0
SPIN 6 IT

-----------------
The next level will be same as level 2 except that you will use A2 instead of A1 and there is really not limit to the number of levels you can make. This process actually starts creating an infinite object: A fractal.

--------------------------------
Once you get the idea it you will feel some change in your brain but you cannot really force it. It has to happen naturally. This is why I do not judge you by your performance but by the effort you put into it and sometime to much pushing does not help. Still avoiding it does not help either. I suggest that you practice and I will give you a test in class (not on paper) to be able to [produce a similar picture. This will motivate you much more than a paper test and I think you will learn better. I will try to give you more examples later and/or in class to allow you to practice more but once you master it the benefit will carry much further than just this math class.

--Dani




1.

















2.














3.

The Web In The Sea Fishbowl #1

You ideas here :)

A Whole New Mind Fishbowl #1

Your ideas here :)

week 9/30 hw due october 7 5:00 pm

This week we will review and explain the seelogo picture problems.

You are asked to do the following 3 pictures: Mastery levels:
1. 75% 2. 85% 3. 100%

1.















2.














3.

Twin Class & You

Activities to do during labyrinth.

Partial plan for today and activities for the weekend

1. Meaning and definition of Fibonacci sequence

2. Definition and meaning of Golden Rectangle

3. Creating a movie in seelogo that shows the connection between the two in a visual way.

It displays the Fibonacci sequence slowly (using the WAIT command, also
local x y z repeat GOMV WRNUM ?)
possibly writes some explanations (using JT and WR commands)
uses the answer to define the dimension of the golden rectangle and draws it
creates art based on golden rectangle.

Look forward to read what happened over weekend.