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Wavemechanic,
your above mentioned citation from "Windows on Wallstreet" could not say itbetter. There you have the problem explained exactly as it stands. This should convince you that in fact you want scaling-independent crossing points. You get proper scaling-independent crossing points when you use the definition that Dimitris has given for the arc. This is valid despite the (inevitable by the way) fact that upon rescaling of one axis you get "illegal" circles, as you like to call ellipses. The term "illegal circle" for an ellipse is not very common in mathematics though.
Rather than doing things just "mechanically", it is important to understandwhat was the original intention of the Fibonacci "circles", or "ellipses" as they should have better called them.
Regards
Alf
----- Original Message -----
From: wavemechanic
To: amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, August 14, 2001 12:36 AM
Subject: Re: [amibroker] Cycles
Dimitris:
(I assume that Cycles = Circles)
Well not quite the "last lines." Your algebra and geometry in this and previous notes are flawless, and you clearly have conquered the equation of a circle without doing harm to the work of the ancients. But that was never the question.
What you have said about programming and displaying a circle is exactly right. However, it is essential to understand a tool and how it is used before programming it. As you have discussed and shown, if you plot relative to the X & Y axis you usually get an ellipse. This, however, is not what you want, which is the reason that software with canned Fibonacci arcs plot relative to screen coordinates so that a circle is displayed. Why do you suppose that virtually all charting programs plot circular arcs at all magnifications and time periods? This is not a matter of mathematics or programming.
The problem with not plotting relative to the screen reflects the dual purpose that arcs are used for. The first function is to identify support and resistance and the second is to interact properly with line studies, in each case providing price and time projections. Both of these have to be effected by plotting relative to screen coordinates. Hopefully, a picture isworth a thousand words. The attached schematic clearly indicates that a circle on the screen is not the same as an ellipse with respect to either ofthese functions. In this simple example, it is clear that the circular arc has provided resistance as it should. Also, although I did not draw it in, it is easy to imagine a line study (e.g., a tangential line) producing very different projections for the circle and ellipse. As I said in my Circular Fibonacci Arc note, one can use any shape on the screen that one wants. However, based on experience circular is the way to go, and in this business, correlations are all that we have.
Remember that these techniques were used back when everything was plottedby hand. It is up to commercial programmers to duplicate these conditions. Unless this is done one is dealing with an entirely different, untested "animal" that may or may not be better. So far, this is not the route followed by software suppliers. Of course, the individual can always choose a different path and customize the arcs, especially with currently available programs, such as AmiBroker, that are relatively easy to program.
The internet is loaded with discussions and examples of Fibonacci Arcs with and without line studies. If you are interested in this subject, it would be worth your time to read about it, as well as note how other charting programs handle the circular vs elliptical arc issue. To speed the processup for you and others, I copied some charts from a variety of sites. Superimpose on these images an elliptical arc and see whether it works as well as circular with respect to support/resistance and interaction with line studies. Perhaps this exercise will result in improved arc formulation, use,and interpretation.
Hope this helped you.
Bill
Market Analyst II
Windows on Wallstreet
A common technique is to display both Fibonacci Arcs and Fibonacci Fan Lines and to anticipate support/resistance at the points where the Fibonacci studies cross. Note that the points where the Arcs cross the price data will vary depending on the scaling of the chart, because the Arcs are drawn sothey are circular relative to the chart paper or computer screen.The following British Pound chart illustrates how the arcs can provide support and resistance (points "A," "B," and "C").
Trendsoft
Arcs combine time and price to display expected containment of price action over time. Circles are used to identify the significant high and low used for these indicators. Note how prices found support, after the significant high at the outer arc.
Many analysts use arcs and fan lines together expecting significant
support or resistance to occur where these lines cross.
Stockhouse
----- Original Message -----
From: Dimitris Tsokakis
To: amibroker@xxxxxxxxxxxxxxx
Sent: Monday, August 13, 2001 3:19 PM
Subject: [amibroker] Cycles
Dear Bill,
Besides what analysts may say through you, here is the last lines
on the subject.
Open ANY textbook to read the equation of a circle.
The happy condition is that we all agree on that the last 2500 years
(x-x0)^2+(y-y0)^2=R^2
where x0, y0 the coordinates of the center and R the radius.
This, in order to be graphed, must be solved for y and come in the
form y=f(x).
The solution is
y=y0+sqrt(R^2-(x-x0)^2
y=y0-sqrt(R^2-(x-x0)^2
(ask the nearest Math Department if you doubt for the solution)
For a day graph we use here
x=cum(1);
(this is the independent variable x=1, 2, 3, etc)
and the code to graph a circle, centered at (380,0) with R=20
is
/*CYCLE*/
x0=380;
y0=0;
R=20;
x=cum(1);
y1=y0+sqrt(R^2-(x-x0)^2);
y2=y0-sqrt(R^2-(x-x0)^2);
graph0=y1;
graph1=y2;
graph1barcolor=graph0barcolor=2;
The result is graphed t w i c e in attached gif.
Exactly the same cycle.
What you see is a cycle, has the math properties of a cycle
and obeys the common for the whole world equation of a
cycle.
With this you may solve a lot of problems, especially if you
are interested for the points this circle cuts other lines,
because it is the equation of the cycle
This note in addition to #3825 Re:Angles is covering the
subject sufficiently enough.
If you mind for the visual part, I have nothing more to add.
Friendly yours
Dimitris Tsokakis
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
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<META content="MSHTML 5.50.4522.1800" name=GENERATOR>
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<DIV>"...Note that the points where the Arcs cross the price data will vary
depending on the scaling of the chart, because the Arcs are drawn so they are
circular relative to the chart paper or computer screen. ..."</DIV>
<DIV> </DIV>
<DIV><FONT size=2>Wavemechanic,</FONT></DIV>
<DIV>your above mentioned citation from "Windows on Wallstreet" could not say it
better. There you have the problem explained exactly as it stands. This should
convince you that in fact you want scaling-independent crossing points. Youget
proper scaling-independent crossing points when you use the definition that
Dimitris has given for the arc. This is valid despite the (inevitable by the
way) fact that upon rescaling of one axis you get "illegal" circles, as youlike
to call ellipses. The term "illegal circle" for an ellipse is not very
common in mathematics though. </DIV>
<DIV>Rather than doing things just "mechanically", it is important to understand
what was the original intention of the Fibonacci "circles", or "ellipses" as
they should have better called them.</DIV>
<DIV> </DIV>
<DIV>Regards</DIV>
<DIV>Alf </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
wavemechanic
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=amibroker@xxxxxxxxxx
href="mailto:amibroker@xxxxxxxxxxxxxxx";>amibroker@xxxxxxxxxxxxxxx</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, August 14, 2001 12:36
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [amibroker] Cycles</DIV>
<DIV><BR></DIV>
<DIV><STRONG><FONT size=2>Dimitris:</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>(I assume that Cycles =
Circles)</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Well not quite the "last lines." Your algebra
and geometry in this and previous notes are flawless, and you clearly have
conquered the equation of a circle without doing harm to the work ofthe
ancients. But that was never the question.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>What you have said about programming and
displaying a circle is exactly right. However, it is essentialto
understand a tool and how it is used before programming it. As you have
discussed and shown, if you plot relative to the X & Y axis you usually
get an ellipse. This, however, is not what you want, which is the reason
that software with canned Fibonacci arcs plot relative to screen coordinates
so that a circle is displayed. Why do you suppose that virtually all
charting programs plot circular arcs at all magnifications and time
periods? This is not a matter of mathematics or
programming.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>The problem with not plotting relative to the
screen reflects the dual purpose that arcs are used
for. The first function is to identify support and resistance
and the second is to interact properly with line studies, in each case
providing price and time projections. Both of these have to be
effected by plotting relative to screen coordinates. Hopefully, a
picture is worth a thousand words. The attached
schematic clearly indicates that a circle on the screen is not the same
as an ellipse with respect to either of these functions. In this simple
example, it is clear that the circular arc has provided resistance as it
should. Also, although I did not draw it in, it is easy to imagine a
line study (e.g., a tangential line) producing very different projectionsfor
the circle and ellipse. As I said in my Circular Fibonacci Arc note, one
can use any shape on the screen that one wants. However, basedon
experience circular is the way to go, and in this business, correlations
are all that we have.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Remember that these techniques were used
back when everything was plotted by hand. It is up to
commercial programmers to duplicate these conditions. Unless this
is done one is dealing with an entirely different, untested "animal"that
may or may not be better. So far, this is not the route followed by
software suppliers. Of course, the individual can always choose a
different path and customize the arcs, especially with currently available
programs, such as AmiBroker, that are relatively easy to
program.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG><STRONG><FONT
size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>The internet is loaded with discussions and examples
of Fibonacci Arcs with and without line studies. If you are interested
in this subject, it would be worth your time to read about it, as
well as note how other charting programs handle the circular vs
elliptical arc issue. To speed the process up for you and others, I
copied some charts from a variety of sites. Superimpose on these images
an elliptical arc and see whether it works as well as circular with respect to
support/resistance and interaction with line studies. Perhaps this
exercise will result in improved arc formulation, use, and
interpretation.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Hope this helped you.</FONT></STRONG></DIV>
<DIV> </DIV>
<DIV><STRONG><FONT size=2>Bill</FONT></STRONG></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2> </FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2>Market Analyst II</DIV>
<P><SPAN style="FONT-WEIGHT: normal; TEXT-DECORATION: none"><IMG height=354
hspace=0 src="http://www.marketanalyst.com.au/help/FA.gif"; width=526
border=0></SPAN></P></FONT></STRONG>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Windows on Wallstreet</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV>
<P>A common technique is to display both Fibonacci Arcs and Fibonacci Fan
Lines and to anticipate support/resistance at the points where the Fibonacci
studies cross. Note that the points where the Arcs cross the price data will
vary depending on the scaling of the chart, because the Arcs are drawn sothey
are circular relative to the chart paper or computer screen.The following
British Pound chart illustrates how the arcs can provide support and
resistance (points "A," "B," and "C").</P>
<CENTER><IMG height=263
src="http://www.geocities.com/WallStreet/Floor/1035/fibonaccistudies-1.gif";
width=380 border=1></CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<CENTER>
<P align=left><FONT face=Palantino,Times,Helvetica,Arial
size=3>Trendsoft</FONT></P>
<P align=left><FONT face=Palantino,Times,Helvetica,Arial size=3>Arcs combine
time and price to display expected containment of price action over time.
Circles are used to identify the significant high and low used for these
indicators. Note how prices found support, after the significant high at the
outer arc.</FONT></P>
<P><FONT face=Palantino,Times,Helvetica,Arial size=3>
<CENTER>
<P><IMG height=319 src="http://www.trendsoft.com/tasc/images/fib2.gif";
width=465> <BR><BR>Many analysts use arcs and fan lines together expecting
significant <BR>support or resistance to occur where these lines
cross.</P></CENTER></FONT></CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<DIV align=left><STRONG><FONT size=2>Stockhouse</FONT></STRONG></DIV>
<DIV align=left><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV align=left><BR></DIV>
<P align=left>
<DIV align=center><IMG height=309 alt=""
src="http://www.stockhouse.com/shfn/aug00/images/slumberger_windowonwallstreet_chart1.gif";
width=527 border=0></DIV>
<DIV align=center><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV align=left><STRONG><FONT size=2></FONT></STRONG> </DIV></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=TSOKAKIS@xxxx href="mailto:TSOKAKIS@xxxx";>Dimitris
Tsokakis</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=amibroker@xxxxxxxxxxxx
href="mailto:amibroker@xxxxxxxxxxxxxxx";>amibroker@xxxxxxxxxxxxxxx</A></DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, August 13, 2001 3:19
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [amibroker] Cycles</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Dear Bill,</FONT></DIV>
<DIV><FONT face=Arial size=2>Besides what analysts may say through you, here
is the last lines</FONT></DIV>
<DIV><FONT face=Arial size=2>on the subject.</FONT></DIV>
<DIV><FONT face=Arial size=2>Open ANY textbook to read the equationof a
circle.</FONT></DIV>
<DIV><FONT face=Arial size=2>The happy condition is that we all agree on
that the last 2500 years</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>(x-x0)^2+(y-y0)^2=R^2</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>where x0, y0 the coordinates of the center and
R the radius.</FONT></DIV>
<DIV><FONT face=Arial size=2>This, in order to be graphed, must be solved
for y and come in the</FONT></DIV>
<DIV><FONT face=Arial size=2>form y=f(x).</FONT></DIV>
<DIV><FONT face=Arial size=2>The solution is</FONT></DIV>
<DIV><FONT face=Arial size=2>y=y0+sqrt(R^2-(x-x0)^2</FONT></DIV>
<DIV><FONT face=Arial size=2>y=y0-sqrt(R^2-(x-x0)^2</FONT></DIV>
<DIV><FONT face=Arial size=2>(ask the nearest Math Department if you
doubt for the </FONT><FONT face=Arial size=2>solution)</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>For a day graph we use here</FONT></DIV>
<DIV><FONT face=Arial size=2>x=cum(1);</FONT></DIV>
<DIV><FONT face=Arial size=2>(this is the independent variable x=1, 2, 3,
etc)</FONT></DIV>
<DIV><FONT face=Arial size=2>and the code to graph a circle, centered at
(380,0) with R=20</FONT></DIV>
<DIV><FONT face=Arial size=2>is</FONT></DIV>
<DIV><FONT face=Arial size=2>/*CYCLE*/</FONT></DIV>
<DIV><FONT face=Arial
size=2>x0=380;<BR>y0=0;<BR>R=20;<BR>x=cum(1);<BR>y1=y0+sqrt(R^2-(x-x0)^2);<BR>y2=y0-sqrt(R^2-(x-x0)^2);<BR>graph0=y1;<BR>graph1=y2;<BR>graph1barcolor=graph0barcolor=2;</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>The result is graphed t w i c e in
attached gif.</FONT></DIV>
<DIV><FONT face=Arial size=2>Exactly the same cycle.</FONT></DIV>
<DIV><FONT face=Arial size=2>What you see is a cycle, has the math
properties of a cycle</FONT></DIV>
<DIV><FONT face=Arial size=2>and obeys the common for the whole world
equation of a </FONT></DIV>
<DIV><FONT face=Arial size=2>cycle.</FONT></DIV>
<DIV><FONT face=Arial size=2>With this you may solve a lot of problems,
especially if you</FONT></DIV>
<DIV><FONT face=Arial size=2>are interested for the points this circle cuts
other lines, </FONT></DIV>
<DIV><FONT face=Arial size=2>because it is the equation of the
cycle</FONT> </DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>This note in addition to #3825 Re:Angles is
covering the</FONT></DIV>
<DIV><FONT face=Arial size=2>subject sufficiently enough.</FONT></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>If you mind for the visual part, I have nothing
more to add.</FONT></DIV></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Friendly yours</FONT></DIV>
<DIV><FONT face=Arial size=2>Dimitris Tsokakis</FONT></DIV><BR><TT>Your use
of Yahoo! Groups is subject to the <A
href="http://docs.yahoo.com/info/terms/";>Yahoo! Terms of Service</A>.</TT>
<BR></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>
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