I made multiple different trials. Major change is adding trigrams and changing codes a bit for the circles.

I realized that I was using two different references for the flag. Both are correct; one I used for my second version, it shows ratios for the measurment, using something like 1, (1/2), (1/4). The one Dr. Proctor shared with me was using bigger numbers for the measurement such as 12, 24, and 6.
When I realized that the taeguk pattern is much bigger than it should be when I draw 건(gun), I realize that my code needs to be revised to make my circles smaller.
I had to think of the usage of 'wdith' and 'unit' in the code. It took a while for me to figure things out.
I did not want to change the fuction Dr. Proctor created, so I make adjustment of my previous work.
I think of how this work would related to math learning or appying math skills. I used arc tangent to figure the angle I need to make for a turtle. I use the center of the big circle as one of a vertex of a right triangle and use the measurement of right trangle (with base 36 and height 24). That's how I got 33.69 degrees, and this was important information for me to move my turtle to the starting point of Dr. Proctor's Trigram fuction.
A strategy I used consistently is that making lots of sketchy work on the piece of paper.
I think of a couple different ways to do math using Taegukgi for elementary or middle schooler. So far just ideas, but I am hoping I can make actual lesson plans and use as an example for an culturally relevant lessons in math class. We can start with korean Flag, but I am sure there are many different flags we can try as well.
I have not been able to make any motions in this drawing project. I wonder if I can make the flag to be waved or try to make the flag looking like fluttering in the wind, but I am pretty sure it requires much more advanced skills.
I am sure I probably have many typos and mistakes here, but somehow this black screen for code makes me care less about me making typoes and errors. haha, I don't know why,  but typing here feels very different from typing on word or google doc.
This activity makes me feel much more comfortable to do 'try and see' without having a clear plan. I did many small changes and see how little changes I made worked or not worked.

drawing old.py

@@ -0,0 +1,28 @@
+# drawing.py
+# ----------
+# By Seoyeon___________
+#
+# (second trial_use fuction_center of Korean flag with two colors)
+
+from turtle import * 
+def tadpole (radius,colour):  # "I name half of yinyang shape tadpole"
+    color("black", colour)   # British spellings for colour to distinguish this from color" 
+    begin_fill()
+    circle(radius,180)  # half circle
+    circle(-radius,180)  # another half circle
+    circle(-radius*2,180)
+    end_fill() 
+
+right(15)
+left(90)
+tadpole (40, "red")
+right(90)
+penup()
+forward(160)
+pendown()
+left(90)
+tadpole (40, "blue")
+
+input()
+
+

drawing.py

@@ -2,31 +2,62 @@
 # ----------
 # By Seoyeon___________
 #
-# (basic practice prior to yin-yang shape.)
+# (Final Version_adding trigram, adding color code)
 
 from turtle import * 
-color("black", "red")
+from trigram import draw_trigram
+def tadpole (width,colour):  # "I name half of yinyang shape tadpole"
+    color("black", colour)   # British spellings for colour to distinguish this from color" 
     begin_fill()
-forward(40)
-right(90)
-forward(20)
-right(90)
-forward(40)
-right(90)
-forward(20)
+    circle(1/2 * width,180)  # half circle
+    circle(-1/2 * width,180)  # another half circle
+    circle(-1 * width,180)
     end_fill() 
 
+width=100
 penup()
-backward(20)
-right(180)
-color("black","blue")
-begin_fill()
-forward(20)
+forward(1/2 * width)
+right(90)
+forward(1*width)
 left(90)
-forward(40)
 left(90)
-forward(20)
-end_fill()
+circle(-2 * width, 33.69)
+pendown()
 
+tadpole (width, "#CD2E3A")
+right(90)
+penup()
+forward(2* width)
+pendown()
+left(90)
+tadpole (width, "#0047A0")
+
+left(90)
+penup()
+forward(1/2 * width)
+pendown()
+
+draw_trigram ([True, True, True], width)
+
+
+right(180)
+penup()
+forward( (6+12+12+6) / 12 * width)
+draw_trigram ([False, False, False], width)
+
+left(90)
+penup()
+circle(18 /12 * width, 33.69*2)
+right(90)
+draw_trigram ([False, True, False], width)
+
+right(180)
+penup()
+forward( (6+12+12+6) / 12 * width)
+draw_trigram ([True, False, True], width)
 input()
 
+
+
+
+

drawing_old.py

@@ -0,0 +1,28 @@
+# drawing.py
+# ----------
+# By Seoyeon___________
+#
+# (second trial_use fuction_center of Korean flag with two colors)
+
+from turtle import * 
+def tadpole (radius,colour):  # "I name half of yinyang shape tadpole"
+    color("black", colour)   # British spellings for colour to distinguish this from color" 
+    begin_fill()
+    circle(radius,180)  # half circle
+    circle(-radius,180)  # another half circle
+    circle(-radius*2,180)
+    end_fill() 
+
+right(15)
+left(90)
+tadpole (40, "red")
+right(90)
+penup()
+forward(160)
+pendown()
+left(90)
+tadpole (40, "blue")
+
+input()
+
+

test_trigram.py

@@ -0,0 +1,12 @@
+from turtle import left
+from trigram import (
+    draw_trigram, 
+    건, 
+    곤,
+    리,
+    감,
+)
+
+left(90)
+draw_trigram([True,False,False], 200)
+input()

trigram.py

@@ -0,0 +1,56 @@
+from turtle import *
+
+건 = [True, True, True]
+곤 = [False, False, False]
+리 = [True, False, True]
+감 = [False, True, False]
+
+def draw_trigram(pattern, width):
+    """Draws a trigram from the Korean flag. 
+    The starting and ending point is the center of the bottom of 
+    the trigram, with the turtle facing up.
+    The pattern should be a list of True/False values, indicating
+    whether each bar should be solid, starting from the top.
+    """
+    unit = width/12
+    for bar_type in pattern:
+        draw_trigram_bar(bar_type, width)
+        fly(unit * 3)
+    fly(unit*-9)
+
+def draw_trigram_bar(is_solid, width):
+    """Draws a single bar from a trigram, starting and ending at the center 
+    of the bottom of the bar.
+    """
+    unit = width/12
+    right(90)
+    fly(unit*-6)
+    if is_solid:
+        draw_black_rectangle(unit*12, unit*2)
+        fly(width/2)
+    else:
+        draw_black_rectangle(unit*5.5, unit*2)
+        fly(unit*6.5)
+        draw_black_rectangle(unit*5.5, unit*2)
+        fly(unit*-0.5)
+    left(90)
+
+def draw_black_rectangle(width, height):
+    """Draws a filled black rectangle, starting and ending at the bottom 
+    left corner and turning to the left.
+    """
+    color('black')
+    fillcolor('black')
+    begin_fill()
+    for half in range(2):
+        forward(width)
+        left(90)
+        forward(height)
+        left(90)
+    end_fill()
+
+def fly(steps):
+    "Move without drawing"
+    penup()
+    forward(steps)
+    pendown()