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But, here is not the same.
x?x axis is time and for a daily graph the unit is 1 day.
y?y axis is price and the unit is 1 USD or 1 EURO or 1 
unit of Dow Jones scale etc.
A square in Analytic Geometry means 4 right angles and 
all sides equal (RELATED TO THE SAME UNIT)
A square here has two sides equal to 35 USD and two sides
equal to 25 DAYS.
To ask 4 sides equal is nonsense.

But, if you want to forget the Euclidean dream and if you want
the deal with REAL properties, there is a solution.
In att. gif we have
tA=282 days
tB=302 days
tB-tA=40 days
highB=6.56 euros
lowA=4.56 euros
gain=2 euros

The ratio R=gain/(tB-tA)=0.05 will be independent of any shape
of your graph, you may call it "tangent" of the hypothetical "angle"
and use it as a measure for further correlations for the same stock.
If in the next uptrend the stock gains 1.5 euro in 30 days, then this
ratio will be 0.05 and the "angles" will look the same on any graph
at any scale.
Just keep in mind that this "angle" will never have a relation with
Euclidean angles and any sin, cosin or atan function will NOT give
the expected results.

No matter if we like it or not, Euclidean Geometry presupposes
common measure for both axis.

Dimitris Tsokakis


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<DIV><FONT face=Arial size=2>In att gif A is a local minimum and B is alocal 
maximum.</FONT></DIV>
<DIV><FONT face=Arial size=2>The two graphs are EXACTLY the same "Price" 
graph</FONT></DIV>
<DIV><FONT face=Arial size=2>for the selected stock.</FONT></DIV>
<DIV><FONT face=Arial size=2>The angle at the above graph looks like a fine 45 
deg.</FONT></DIV>
<DIV><FONT face=Arial size=2>The same angle in below graph looks like 30 
deg.</FONT></DIV>
<DIV><FONT face=Arial size=2>What is the real angle and how will be thesame for 
</FONT></DIV>
<DIV><FONT face=Arial size=2>both graphs.</FONT></DIV>
<DIV><FONT face=Arial size=2>Is there any "standard" ratio that we should follow 
with</FONT></DIV>
<DIV><FONT face=Arial size=2>the accuracy of Euclidean Geometry in angles 
design?</FONT></DIV>
<DIV><FONT face=Arial size=2>Is there any "standard" goniometer superimposed on 
</FONT></DIV>
<DIV><FONT face=Arial size=2>the "standard" graph, in order to trace the 
"accurate"</FONT></DIV>
<DIV><FONT face=Arial size=2>45 deg line?</FONT></DIV>
<DIV><FONT face=Arial size=2>Of course not.</FONT></DIV>
<DIV><FONT face=Arial size=2>Angles, as two dimensional objects change their 
visual</FONT></DIV>
<DIV><FONT face=Arial size=2>shape according to the climax of each 
axis.</FONT></DIV>
<DIV><FONT face=Arial size=2>And here is a great misunderstanding.</FONT></DIV>
<DIV><FONT face=Arial size=2>In Analytic Geometry, the x&acute;x and y&acute;y axis 
represent the </FONT></DIV>
<DIV><FONT face=Arial size=2>same set of Real numbers, so they have thesame 
unit 1</FONT></DIV>
<DIV><FONT face=Arial size=2>and the line from (0,0) to (3,3) will ALWAYS have 
angle 45 deg.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>But, here is not the same.</FONT></DIV>
<DIV><FONT face=Arial size=2>x&acute;x axis is time and for a daily graph the unit is 
1 day.</FONT></DIV>
<DIV><FONT face=Arial size=2>y&acute;y axis is price and the unit is 1 USD or 1 EURO 
or 1 </FONT></DIV>
<DIV><FONT face=Arial size=2>unit of Dow Jones scale etc.</FONT></DIV>
<DIV><FONT face=Arial size=2>A square in Analytic Geometry means 4 right angles 
and </FONT></DIV>
<DIV><FONT face=Arial size=2>all sides equal (RELATED TO THE SAME 
UNIT)</FONT></DIV>
<DIV><FONT face=Arial size=2>A square here has two sides equal to 35 USD and two 
sides</FONT></DIV>
<DIV><FONT face=Arial size=2>equal to 25 DAYS.</FONT></DIV>
<DIV><FONT face=Arial size=2>To ask 4 sides equal is nonsense.</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>But, if you want to forget the Euclidean dream and 
if you want</FONT></DIV>
<DIV><FONT face=Arial size=2>the deal with REAL properties, there is a 
solution.</FONT></DIV>
<DIV><FONT face=Arial size=2>In att. gif we have</FONT></DIV>
<DIV><FONT face=Arial size=2>tA=282 days</FONT></DIV>
<DIV><FONT face=Arial size=2>tB=302 days</FONT></DIV>
<DIV><FONT face=Arial size=2>tB-tA=40 days</FONT></DIV>
<DIV><FONT face=Arial size=2>highB=6.56 euros</FONT></DIV>
<DIV><FONT face=Arial size=2>lowA=4.56 euros</FONT></DIV>
<DIV><FONT face=Arial size=2>gain=2 euros</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>The ratio R=gain/(tB-tA)=0.05 will be independent 
of any shape</FONT></DIV>
<DIV><FONT face=Arial size=2>of your graph, you may call it "tangent" of the 
hypothetical "angle"</FONT></DIV>
<DIV><FONT face=Arial size=2>and use it as a measure for further correlations 
for the same stock.</FONT></DIV>
<DIV><FONT face=Arial size=2>If in the next uptrend the stock gains 1.5euro in 
30 days, then this</FONT></DIV>
<DIV><FONT face=Arial size=2>ratio will be 0.05 and the "angles" will look the 
same on any graph</FONT></DIV>
<DIV><FONT face=Arial size=2>at any scale.</FONT></DIV>
<DIV><FONT face=Arial size=2>Just keep in mind that this "angle" will never have 
a relation with</FONT></DIV>
<DIV><FONT face=Arial size=2>Euclidean angles and any sin, cosin or atan 
function will NOT give</FONT></DIV>
<DIV><FONT face=Arial size=2>the expected results.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>No matter if we like it or not, Euclidean Geometry 
presupposes</FONT></DIV>
<DIV><FONT face=Arial size=2>common measure for both axis.</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>Dimitris Tsokakis</FONT></DIV>
<DIV>&nbsp;</DIV></BODY></HTML>

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