Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Patti Sun Apr 24, 2011 5:48 pm

Tap uploaded this pretty comprehensive collection of the works of various other dg researchers.

http://www.scribd.com/doc/24044243/Final-Dissertation

They used the same sources as we did to interpret the triradius i.e. mainly Cummins & Midlo, Penrose and Schaumann & Alter.

From page 54:

Dermatoglyphic Landmarks on the fingertip patterns

1. Triradii
2. Cores.
3. Radiants.

1.Triradius: A triradius is formed by confluence of three ridges systems.

Triradius Point: It is the geometric center of the triradius. Ideally it is the meeting point of three ridges, if they fail to meet, the triradial point can be represented by very short, dot like ridge called as island or by a ridge ending or it may lie on a ridge at the point near the center of the divergence of the three innermost ridges. Triradius in such cases is described as extralimital and commonly observed in the hypothenar area of the palm.

2.Core: It is approximate center of the palm. The core may be of different shapes. In ridge counting the point of core (not the whole core) is used.

3.Radiants (type lines): Radiants are ridges that emanate from the triradius and enclose the pattern area.

Two points stand out to me as reflecting how they have combined and interpreted the sources.

"divergence of the three innermost ridges"

They have not said 2 innermost ridges, as did the FBI, but 3 innermost ridges. This implies to me that they recognize the triangular shape of the 3 ridges meeting at the corners/outer angles, but not attached at the corner. As we see in Fig. 3.5 E below:

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 3-12-212

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 3-12-212

The other is:

"Triradius in such cases is described as extralimital and commonly observed in the hypothenar area of the palm."

They did not describe "such cases" prior to that sentence. So either they edited out a few sentences here or didn't realize that the triradial point when found on other locations, such as the dot etal., was not necessarily involving an extralimital triradius. Smile

I posted this as an illustration how each of us can seriously study the same resource material and individualize our interpretations.

**Lynn** Mon Apr 25, 2011 1:11 am

Patti wrote:I also do not think there is any discrepancy between Cummins & Midlo, Penrose, and Schaumann & Alter in their descriptions of the triradii. All relate to the coming together of three different fields of parallel ridges. All relate to configurations that involve angles nearly equal at 120 degrees. Both Schaumann & Alter and Cummins & Midlo describe clearly the either/or nature of these fields meeting in the form of ridges that meet at the outer angles or ridges that meet in a common center. Penrose illustrates this in 3 simple illustrations, and Schaumann & Alter expand the basic formations to illustrate what I interpret as the typical variants.

catching up on this thread....I agree with you here Patti.

**Lynn** Mon Apr 25, 2011 1:27 am

Martijn (admin) wrote:

I understand your admiration of the work of Cummins & Midlo - especially since I am a fan of their work as well.

But you suggest that I described some kind of 'discrpancy', but that is not what I tried to describe. My point only relates to the their 'format of presentation' - which I think shows a lack of details - compared to the other works that we have discussed during the past months (Penrose, Schaumann & Alter, and the F.B.I. book).

I will now try to specify where I observe this lack of details exactly:

My problem with Cummins & Midlo's work lies in the fact that did not include specified guidelines for how to identify the triradial point when there is no meeting-point of three ridges.

For example: their index indicates that the issue of the 'triradial point' (point of triradius / point of delta) is only mentioned on page 58. While we now know - with the help of especially the F.B.I. book - that the identification of the 'triradial point' is really a complex issue, especially when there is no 'triradial' meeting point of three ridges (such as in the fingerprint example where there are multiple bifurcations that could serve as the delta, etc.).

For our purposes (as handreaders) in locating triradial point, I think Cummins & Midlo give pretty clear instructions on page 58. As you rightly say, the FBI give more detailed instructions on how to find the delta (which is the same as the 'triradial point'.)

So, I haven't found any conflicting materials in Cummins & Midlo's work (when compared to the other works). However I do observe that their work does not include likewise details as described in the works of Penrose, Schaumann & Alter, and the F.B.I.

I guess this lack of details regarding the issue of how to ídentify the 'triradial point'... is probably a direct result of that they present their theories in the perspective of Galton's system and Henry's system.

I hope my specification is helpfull for you to recognize that my point directly relates to how the 'art of fingerprint interpretation' has continued to evolve after Cummins & Midlo presented their work.

I understand what you are saying about how it evolved since Cummins & Midlo's work. But if we look at them in conjunction with Penrose, Schaumann & Alter, and the F.B.I. we have a LOT of info, I agree still some slightly grey areas, but also some main things in common Smile

**Lynn** Mon Apr 25, 2011 1:31 am

Patti wrote:Then basically what you are saying is that you think that Cummins & Midlo failed to describe the triradial point?

I think the first paragraph might be confusing to some. They imply that at the time the book was written, those in the field used the term "delta" to mean the same as "triradius". As a synonym. In the first sentence they say there is a distinction between the two.

The word delta was based on the Greek letter for the 4th letter of their alphabet and because of it's shape became commonly used for a triangular shape.

C & M explain that because a triangular shape isn't always present, sometimes instead you'll find the 3 ridges meeting at a center point, the word "delta" is not used to mean "triradius".

I think all of the resources are telling us that the triradius itself is 3 ridges. 1 ridge from each field that converge upon each other. The three innermost ridges.

C & M say there's the "delta" shape and the "three ridges radiating from a common point" shape triradius.

So far nothing different here than in Penrose or Schaumann & Alter.

Then C & M tell us about the triradial point. In the case of the ridges radiating from a common point, the triradial point is the meeting location. Then in the "corresponding locus" or the location of the triradial point in the "delta" or triangular shape, they are not specific but 'assume' the reader can figure it out by working with simple triradii first, and when you have the concept, you can figure out more complicated patterns.

For me, I would think that since in the type where 3 ridges meet at the center, the center is the triradial point - we are trying to find the center of the other formations of triradii (3 innermost ridges). If it's a delta shape, then it'd be in the center of the triangular shape.

The FBI's rules show that when there is no "dot" in this area to move to the ridge wall beyond that central location.

You mention that this triangular shape is rarely seen. I think it is less commonly seen with all 3 corners touching. More often these outer corners are meeting each other in the form of converging parallel ridges.

Again, nothing different here. A triradial point is the center location of either the 3 ridges meeting at the corners or 3 ridges meeting at a common point. If the pattern isn't so clean cut and you have fragmental ridges we can use the rules by the FBI or figure out what looks like the center of 3 ridge fields meeting as suggested by C & M and illustrated by Schaumann & Alter.

They move on to radiants and continue with instructions for the two types of triradii. If it's the 3 ridges meeting, just trace each ridge. When it's the pattern where they meet at the outer corners you follow the ridge where it meets at the angle according to the rule for it's location in respect to the pattern area. Both locations of tracing the triradial point results in the same ridges being traced as the radiants.

I think they have actually described in detail what to look for and how to proceed with what you find more so than the other two sources. Penrose's precise description narrows down what to look for and Schaumann & Alter give you some alternatives or variations to the patterns, which Cummins & Midlo did with actual prints, but left it up to us to study and figure out the differences.

Patti,

I can follow everything you are saying, and I find nothing to disagree with. It seems the same as I have understood it.

**Lynn** Mon Apr 25, 2011 2:08 am

Patti wrote:
Martijn (admin) wrote:
And yes, in return I can agree about your second statement above because Cummins & Midlo do mention all essential elements (including that the pattern area requires to be known in order to trace the radiants).

You've mentioned this before regarding the pattern area needs to be known in order to trace the radiants.

I think they say just the opposite.

To me it's sort of like 'connect the dots'. You don't truly see the precise pattern area until after the radiants are drawn.

Cummins and Midlo state on top of Pg. 57:

"These type lines, traced on the print according to conventions which are to be defined, are the radiants extended from the two triradii. The area enclosed by the type lines (but continuously enclosed on in the meet whorl, to be characterized later) is the pattern area. the type lines are appropriately termed the skeleton of the pattern. The form and design of the pattern are suggested by the skeleton, much as the bony framework of an animal gives a clue to the form of that animal in the flesh."

They continue to define the area above and below the pattern. Which implies that once you have made your outline, you can then determine the pattern from the distal and proximal transverse system.

(I've skipped a few posts in reading/replying)
Martijn, I agree with Patti here. If you view the whole fingerprint, then tracing the radiants from the triradius (or triradial area) are the things that make the pattern obvious. You don't need to know where the pattern is before you draw the radiants. The radiants define, or outline, or enclose, the pattern.

However, you cannot draw any conclusions about the pattern when you only have a triradial area to look at (eg the Schaumann & Alter / Penrose '6 examples of ridges within the area of triradius').

**Martijn (admin)** Mon Apr 25, 2011 11:56 am

Lynn wrote:
Patti wrote:
Martijn (admin) wrote:
And yes, in return I can agree about your second statement above because Cummins & Midlo do mention all essential elements (including that the pattern area requires to be known in order to trace the radiants).

You've mentioned this before regarding the pattern area needs to be known in order to trace the radiants.

I think they say just the opposite.

To me it's sort of like 'connect the dots'. You don't truly see the precise pattern area until after the radiants are drawn.

Cummins and Midlo state on top of Pg. 57:

"These type lines, traced on the print according to conventions which are to be defined, are the radiants extended from the two triradii. The area enclosed by the type lines (but continuously enclosed on in the meet whorl, to be characterized later) is the pattern area. the type lines are appropriately termed the skeleton of the pattern. The form and design of the pattern are suggested by the skeleton, much as the bony framework of an animal gives a clue to the form of that animal in the flesh."

They continue to define the area above and below the pattern. Which implies that once you have made your outline, you can then determine the pattern from the distal and proximal transverse system.

(I've skipped a few posts in reading/replying)
Martijn, I agree with Patti here. If you view the whole fingerprint, then tracing the radiants from the triradius (or triradial area) are the things that make the pattern obvious. You don't need to know where the pattern is before you draw the radiants. The radiants define, or outline, or enclose, the pattern.

However, you cannot draw any conclusions about the pattern when you only have a triradial area to look at (eg the Schaumann & Alter / Penrose '6 examples of ridges within the area of triradius').

Hi Lynn,

When taken out of the context of the point that I was making... I actually agree with Patti's words as well! Smile

But in my response to Patti's comments I have explaned why I made the comment described in the red words - actually I took it directly from Cummins & Midlo - I was talking about their definition of the 'radiants', but Patti responded by talking about the definition of the 'type lines'!.

(By the way, Lynn you once have made yourself a likewise point in our discussions about Schaumann & Alter's examples - figure 3.5)

**Martijn (admin)** Mon Apr 25, 2011 12:01 pm

Hi Lynn,

You mentioned that you skipped a few poists, and therefore maybe... you may have missed that Patti and I actually agreed about my essential point that Cummins & Midlo's work can be described as being (far) less detailed regarding describing the crucial element in the triradius: the 'triradial point'.

Basically, I could also say that this is lack of details is illustrated by the fact that Cummins & Midlo have not presented any visual example in which the 'triradial point' is located/marked.

Historically, therefore I could add to my definition the following summarization:

Galton's theory (late 19th century) does not yet mention the essential 'triradial point', and in that perspective Galton's theory is outdated. Cummins & Midlo (1943) have mentioned the importance of the 'triradial point' and they have described some basic guidelines, but advanced guidelines are missing in their work.

Penrose (1950's) and Schaumann & Alter (1976) have described a few more advanced guidelines regarding how to find the 'triradial point' - illustrated with visual examples. And finally, the F.B.I. has described all details regarding how to find the 'triradial point' (they call it the 'delta').

bounce

... My definition for the 'triradius' was basically an attempt to summarize the essential elements, as a logicial next step of the fact that we discovered that the vocabulary used by the various authors can become highly confusing when their words are taken literally.

And in the perspective of our discussions I could summarize that we were confronted with these vocabulary-problems regarding the words: 'delta', 'type lines'... but also regarding the words 'triradius' and 'bifurcation'!!

I hope you & Patti are aware of the problematic aspects of all 4 four words...?

**Lynn** Mon Apr 25, 2011 2:25 pm

Martijn (admin) wrote:because Cummins & Midlo do mention all essential elements[/color] (including that the pattern area requires to be known in order to trace the radiants).

Lynn wrote:Martijn, I agree with Patti here. If you view the whole fingerprint, then tracing the radiants from the triradius (or triradial area) are the things that make the pattern obvious. You don't need to know where the pattern is before you draw the radiants. The radiants define, or outline, or enclose, the pattern.

Of course you are right, we do need to know where the pattern area is to draw the radiants!

"... In following a radiant beyond an interruption of a traced ridge, the tracing is continued on the ridge which is in end-to-end relation, or, if there is no such ridge, the tracing line is transferred to the next ridge on the side away from the interior of the pattern area; similarly, in meeting a bifurcation the tracing is followed on the peripherial branch of the fork."

Martijn wrote:But in my response to Patti's comments I have explaned why I made the comment described in the red words - actually I took it directly from Cummins & Midlo - I was talking about their definition of the 'radiants', but Patti responded by talking about the definition of the 'type lines'!.

But in C&M terminology, they are the same thing.
P57 "These type lines, traced on the print according to conventions which are to be defined, are the radiants extended from the two triradii."
P58 "The triradius has a double importance in finger-print analysis. First, the ridges from it are the three radiants, the type lines above described."

**Martijn (admin)** Mon Apr 25, 2011 3:58 pm

Lynn wrote:
Of course you are right, we do need to know where the pattern area is to draw the radiants!

...

Thanks for making that correction from your side - which implicates that you now recognize that my words (marked red by Patti) are correct.

(Yes, there is no contradiction between Cummins & Midlo's words about their 'type lines' and 'radiants' - basically they are indeed almost the same. Thought there is a small difference... because why else would they have started talking about those issues as two different aspects??? Very Happy

)

Patti Mon Apr 25, 2011 4:25 pm

Lynn wrote:
Martijn (admin) wrote:because Cummins & Midlo do mention all essential elements[/color] (including that the pattern area requires to be known in order to trace the radiants).
Lynn wrote:Martijn, I agree with Patti here. If you view the whole fingerprint, then tracing the radiants from the triradius (or triradial area) are the things that make the pattern obvious. You don't need to know where the pattern is before you draw the radiants. The radiants define, or outline, or enclose, the pattern.

Of course you are right, we do need to know where the pattern area is to draw the radiants!

"... In following a radiant beyond an interruption of a traced ridge, the tracing is continued on the ridge which is in end-to-end relation, or, if there is no such ridge, the tracing line is transferred to the next ridge on the side away from the interior of the pattern area; similarly, in meeting a bifurcation the tracing is followed on the peripherial branch of the fork."

Martijn wrote:But in my response to Patti's comments I have explaned why I made the comment described in the red words - actually I took it directly from Cummins & Midlo - I was talking about their definition of the 'radiants', but Patti responded by talking about the definition of the 'type lines'!.

But in C&M terminology, they are the same thing.
P57 "These type lines, traced on the print according to conventions which are to be defined, are the radiants extended from the two triradii."
P58 "The triradius has a double importance in finger-print analysis. First, the ridges from it are the three radiants, the type lines above described."

I agree with Lynn agreeing with me Laughing

The FBI's outer type lines and the radiants traced from the triradial point (fbi delta) are not counted in the ridge count, both outline the pattern. Most of the time when the radiants are traced they become the same exact ridges as the FBI type lines. (unless the one tracing does not move to the innermost ridges to find the center of the innermost ridges Very Happy

)

Since the terminology is mixed up enough as it is, I think when putting forth a summary and report in the form of a simplified method, it shouldn't be put forth in a way that cannot be reconciled with previously established methods.

By this Martijn, I'm referring to the concept of giving preference to a *bifurcation* and even labeling forked ridges from skinny to fat. This was done without any consideration to how angles are explained in the FBI terminology in regards to forking and abutting ridges with angles from 45 to 90 degrees.

A bifurcation formed in the general development and flow of ridges in a common field or two, is totally different than ridges abutting and/or merging from three different fields.

I think the emphasis on looking for 3 nearly equal angles of 120 degrees (min of 90 degrees) is a rule to help people avoid making the mistake of simply choosing a bifurcation. It appears to me your presentation does the opposite in recommending the bifurcation.

**Lynn** Mon Apr 25, 2011 4:39 pm

Martijn (admin) wrote:Thanks for making that correction from your side - which implicates that you now recognize that my words (marked red by Patti) are correct.

Regarding the red words - yes I think I was confusing 'pattern area' and 'pattern'.
I understand that we need to know where the pattern area is in order to trace the ridges from the radiants - because in case of broken ridges we need to know which are closer to the pattern area in order to draw the continuity.

Regarding Patti's quote "The type lines are appropriately termed the skeleton of the pattern. The form and design of the pattern are suggested by the skeleton,
As Patti said, "Which implies that once you have made your outline, you can then determine the pattern...."

Martijn (admin) wrote:(Yes, there is no contradiction between Cummins & Midlo's words about their 'type lines' and 'radiants' - basically they are indeed almost the same. Thought there is a small difference... because why else would they have started talking about those issues as two different aspects??? )

C&M say "the ridges from it are the three radiants, the type lines above described." which implies that they are the same thing. But Ok, I guess we could say the small difference being that the radiants are the ridges that come from the triradius, and the type lines are the continuation or extension of these ridges.

Patti Mon Apr 25, 2011 4:56 pm

Martijn (admin) wrote:
Lynn wrote:
Of course you are right, we do need to know where the pattern area is to draw the radiants!

...

Thanks for making that correction from your side - which implicates that you now recognize that my words (marked red by Patti) are correct.

(Yes, there is no contradiction between Cummins & Midlo's words about their 'type lines' and 'radiants' - basically they are indeed almost the same. Thought there is a small difference... because why else would they have started talking about those issues as two different aspects??? )

You only have to be aware of the side that you can see recurving ridges. You don't always at a glance see that the recurves are spoiled by appendages until you have enclosed them into the pattern area. As we've intensely discussed these tented arch/loop mix types, it's obvious that the pattern at times cannot accurately be decided until a checklist of rules have been utilized.

The science community is consistent in working with radiants as the type lines. Found by finding 3 innermost ridges from 3 converging fields.

The FBI has us noticing the side the pattern is on and then looking at the two innermost parallel diverging ridges (one from the distal field and one from the proximal field). Looking between those two parallel diverging ridges we find our way to the pattern wall or innermost ridge from the pattern field. Their rules help us get to the innermost area and what to do with what we find there.

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Fig01910

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Fig01910

**Lynn** Mon Apr 25, 2011 5:01 pm

Martijn wrote:And in the perspective of our discussions I could summarize that we were confronted with these vocabulary-problems regarding the words: 'delta', 'type lines'... but also regarding the words 'triradius' and 'bifurcation'!!

I hope you & Patti are aware of the problematic aspects of all 4 four words...?

I am not aware of the problematic aspect of the word 'bifurcation'. It's a splitting ridge.
Tho I am still confused by you saying that a triradius is a bifurcation variant.

**Martijn (admin)** Mon Apr 25, 2011 5:04 pm

Lynn wrote:
Martijn (admin) wrote:Thanks for making that correction from your side - which implicates that you now recognize that my words (marked red by Patti) are correct.

Regarding the red words - yes I think I was confusing 'pattern area' and 'pattern'.
I understand that we need to know where the pattern area is in order to trace the ridges from the radiants - because in case of broken ridges we need to know which are closer to the pattern area in order to draw the continuity.

Lynn, thanks for confirming once again that my words are actually correct.

(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)

Thanks!

Patti Mon Apr 25, 2011 5:09 pm

Martijn (admin) wrote:
Lynn wrote:
Martijn (admin) wrote:Thanks for making that correction from your side - which implicates that you now recognize that my words (marked red by Patti) are correct.

Regarding the red words - yes I think I was confusing 'pattern area' and 'pattern'.
I understand that we need to know where the pattern area is in order to trace the ridges from the radiants - because in case of broken ridges we need to know which are closer to the pattern area in order to draw the continuity.

Lynn, thanks for confirming once again that my words are actually correct.

(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)

Martijn, most people reading this with an interest of learning, would not understand the difference between pattern area and the pattern itself. Perhaps Lynn and my misunderstanding your words could be helpful to you in making it more clear.

**Lynn** Mon Apr 25, 2011 5:11 pm

Martijn (admin) wrote:(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)[/color]

I think the red colour was just to highlight the words in the quote. ??

**Martijn (admin)** Mon Apr 25, 2011 5:16 pm

Lynn wrote:
Martijn wrote:And in the perspective of our discussions I could summarize that we were confronted with these vocabulary-problems regarding the words: 'delta', 'type lines'... but also regarding the words 'triradius' and 'bifurcation'!!

I hope you & Patti are aware of the problematic aspects of all 4 four words...?

I am not aware of the problematic aspect of the word 'bifurcation'. It's a splitting ridge.
Tho I am still confused by you saying that a triradius is a bifurcation variant.

Lynn, I made that comment because of how the F.B.I. is using the word 'bifurcation': at page 9 they have listed six shapes for how a 'delta' (point) can manifest, and the 'bifurcation' is listed at the number one position... which implicates that they describe any 'triradius' as a bifurcation.

And this is for example very explicitely confirmed by the statement for figure 25 (see the picture below):

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Fig025

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Fig025

Quote from the F.B.I. book (page 11/12)

"Figure 25 shows ridge A bifurcating from the lower type line inside the pattern area. Bifurcations are also present within this pattern at points B and C. The bifurcation at the point marked "delta" is the only one which fulfills all conditions necessary for its location."

(Edit: I could add... in this example there are multiple bifurcations, where only one is 'open to the core'; and it is not a coincidence that the delta-bifurcation... looks similar to a 'triradius' - though in the scientific point of view this 'triradial point' - should not be be described as a true 'triradius' because the smallest angle of the 'diverging radiants' is slightly smaller than 90 degrees)

Lynn, do you now understand... ? Very Happy

**Martijn (admin)** Mon Apr 25, 2011 5:22 pm

Lynn wrote:
Martijn (admin) wrote:(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)[/color]

I think the red colour was just to highlight the words in the quote. ??

Quite unlikely ... because immediately after Patti marked my words 'red', she explicitely described that she 'thought' Cummins & Midlo were saying the opposite of what I described - see the quote below.

(And afterwards she presented the quote relating to the 'type lines'... while I was talking about Cummins & Midlo's 'radiants', etc. etc. etc. etc. etc. Wink

)

Patti wrote:
Martijn (admin) wrote:
And yes, in return I can agree about your second statement above because Cummins & Midlo do mention all essential elements (including that the pattern area requires to be known in order to trace the radiants).

You've mentioned this before regarding the pattern area needs to be known in order to trace the radiants.

I think they say just the opposite.

**Lynn** Mon Apr 25, 2011 5:41 pm

Martijn (admin) wrote:Lynn, I made that comment because of how the F.B.I. is using the word 'bifurcation': at page 9 they have listed 6 shaped for how a 'delta' (point) can manifest, and the 'bifurcation' is listed at the number one position... which implicates that they describe any 'triradius' as a bifurcation, see the statement for figure 25 (see the picture below):

Quote from the F.B.I. book (page 11/12)

"Figure 25 shows ridge A bifurcating from the lower type line inside the pattern area. Bifurcations are also present within this pattern at points B and C. The bifurcation at the point marked "delta" is the only one which fulfills all conditions necessary for its location."

Lynn, do you now understand... ?

erm,,,no, not really!

re "which implicates that they describe any 'triradius' as a bifurcation."
but the FBI do not describe triradii at all!

Yes in this example, FBI place the delta at the point where the ridge bifurcates.
But from C&M perspective, the 'delta' is the small triangular shape where the 3 ridge fields join, and the triradial point would be in its centre.

Patti Mon Apr 25, 2011 5:46 pm

Martijn (admin) wrote:
Lynn wrote:
Martijn wrote:And in the perspective of our discussions I could summarize that we were confronted with these vocabulary-problems regarding the words: 'delta', 'type lines'... but also regarding the words 'triradius' and 'bifurcation'!!

I hope you & Patti are aware of the problematic aspects of all 4 four words...?

I am not aware of the problematic aspect of the word 'bifurcation'. It's a splitting ridge.
Tho I am still confused by you saying that a triradius is a bifurcation variant.

Lynn, I made that comment because of how the F.B.I. is using the word 'bifurcation': at page 9 they have listed 6 shaped for how a 'delta' (point) can manifest, and the 'bifurcation' is listed at the number one position... which implicates that they describe any 'triradius' as a bifurcation, see the statement for figure 25 (see the picture below):

Quote from the F.B.I. book (page 11/12)

"Figure 25 shows ridge A bifurcating from the lower type line inside the pattern area. Bifurcations are also present within this pattern at points B and C. The bifurcation at the point marked "delta" is the only one which fulfills all conditions necessary for its location."

Lynn, do you now understand... ?

I see the *bifurcation* at the point marked "delta" (fbi triradial point of course) as the marginal angle of the 3 angles of the triradius that meets at the outer angles. That *birucation* is only 2 ridges of 2 converging fields and not 3.

This Fig. 25 is an example of Penrose's G:
The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Penros11

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Penros11

**Lynn** Mon Apr 25, 2011 5:51 pm

Martijn (admin) wrote:
Lynn wrote:
Martijn (admin) wrote:(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)[/color]

I think the red colour was just to highlight the words in the quote. ??

[color=darkred]Quite unlikely ... because immediately after Patti marked my words 'red', she explicitely described that she 'thought' Cummins & Midlo were saying the opposite of what I described - see the quote below.

well only Patti can tell us if there was any significance to the red colour.

And afterwards she presented the quote relating to the 'type lines'... while I was talking about Cummins & Midlo's 'radiants', etc. etc. etc. etc. etc.

I'm not sure why you have a problem with it? Patti's quote from Cummins & Midlo says
"These type lines, traced on the print according to conventions which are to be defined, are the radiants extended from the two triradii.

**Lynn** Mon Apr 25, 2011 5:53 pm

Patti wrote:I see the *bifurcation* at the point marked "delta" (fbi triradial point of course) as the marginal angle of the 3 angles of the triradius that meets at the outer angles. That *birucation* is only 2 ridges of 2 converging fields and not 3.

yes, that's how I see it.

Patti Mon Apr 25, 2011 6:04 pm

Lynn wrote:
Martijn (admin) wrote:(And I assume that you will also agree with me that Patti better should not have marked my words with the color red)[/color]

I think the red colour was just to highlight the words in the quote. ??

Yes.

**Martijn (admin)** Mon Apr 25, 2011 6:14 pm

Lynn wrote:
erm,,,no, not really!

re "which implicates that they describe any 'triradius' as a bifurcation."
but the FBI do not describe triradii at all!

Yes in this example, FBI place the delta at the point where the ridge bifurcates.
But from C&M perspective, the 'delta' is the small triangular shape where the 3 ridge fields join, and the triradial point would be in its centre.

Lynn, the only reason why the F.B.I. has decided not to use the word 'triradius' (nor the word 'triradial point')... has to be because the concept of how a 'triradius' was defined by earlier researchers (including: Galton, Cummins & Midlo, Penrose & Schaumann & Alter)... became problematic:

Because in their search for a 'sharp' definition, these researchers already had started using a different vocabulary ... after they found that Galton's first attempt did not include the essential element: the 'triradial point' (= the F.B.I.'s delta).

cheers

... Now, maybe this is illustrated by the fact that Danuta Loesch introduced in 1983 another (more specified) definition for the triradius (quoted from 'Quantitative Dermatoglyphics', page 7):

"The triradius is formed when three fields of parallel lines meet and its centre has three radiant lines which lie approximately 120 degrees to one another (in practice, however, singularities in the lines of greatest curvature on a surface may produce unsymmetrical triradii so that the angles between the radiants may not be equal)."

Voila... bounce

...!!!! In Loesch's definition we see a characteristic that can directly be associated with a typical characteristic of how a 'fork'/'splitting' has always been defined - except of course... (1) while in a true 'fork'/'splitting' the two diverging ridges continue parallel... (2) but in a true 'bifurcation' the diverging ridges continue in a different direction... (3) and in a true 'triradius' the diverging ridges continue in a different direction making an angle between 90 and 120 degrees.

And after saying this... I hope it makes sense that next to the words 'triradius' and 'triradial point'... the F.B.I. is also not using the words 'fork' and 'splitting'!!!

Which implicates that the F.B.I. really is using the word 'bifurcation' as an ALTERNATIVE NAME for a group of words, including: the 'triradius', the 'fork' and the 'splitting'!

'Capice?' ... Very Happy

PS. In my former post I have also added an additional comment about figure 25 where I explain a few more details regarding what we can see in that example.

Patti Mon Apr 25, 2011 6:32 pm

Martijn (admin) wrote:
Lynn wrote:
erm,,,no, not really!

re "which implicates that they describe any 'triradius' as a bifurcation."
but the FBI do not describe triradii at all!

Yes in this example, FBI place the delta at the point where the ridge bifurcates.
But from C&M perspective, the 'delta' is the small triangular shape where the 3 ridge fields join, and the triradial point would be in its centre.

Lynn, the only reason why the F.B.I. has decided not to use the word 'triradius' (nor the word 'triradial point')... has to be because the concept of how a 'triradius' was defined by earlier researchers (including: Galton, Cummins & Midlo, Penrose & Schaumann & Alter)... became problematic:

Because in their search for a 'sharp' definition, these researchers already had started using a different vocabulary ... after they found that Galton's first attempt did not include the essential element: the 'triradial point' (= the F.B.I.'s delta).

... Now, maybe this is illustrated by the fact that Danuta Loesch introduced in 1983 another (more specified) definition for the triradius (quoted from 'Quantitative Dermatoglyphics', page 7):

"The triradius is formed when three fields of parallel lines meet and its centre has three radiant lines which lie approximately 120 degrees to one another (in practice, however, singularities in the lines of greatest curvature on a surface may produce unsymmetrical triradii so that the angles between the radiants may not be equal)."

Voila... ...!!!! In Loesch's definition we see a characteristic that can directly be associated with a typical characteristic of how a 'fork'/'splitting' has always been defined - except of course... (1) while in a true 'fork'/'splitting' the two diverging ridges continue parallel... (2) but in a true 'bifurcation' the diverging ridges continue in a different direction... (3) and in a true 'triradius' the diverging ridges continue in a different direction making an angle between 90 and 120 degrees.

And after saying this... I hope it makes sense that next to the words 'triradius' and 'triradial point'... the F.B.I. is also not using the words 'fork' and 'splitting'!!!

Which implicates that the F.B.I. really is using the word 'bifurcation' as an ALTERNATIVE NAME for a group of words, including: the 'triradius', the 'fork' and the 'splitting'!

'Capice?' ...

PS. In my former post I have also added an additional comment about figure 25 where I explain a few more details regarding what we can see in that example.

Whoa Martijn!!!

Note again the confirmation of 120 degrees from Loesch!

A bifurcation is a forking ridge or a ridge splitting. 45 degrees to 90 degrees is 2 ridges abutting.

I think it was misleading for the FBI to refer to the meeting of the distal and proximal fields (when conjoined) as a bifurcation. They did however tell us with their illustration of the two different fields and the enclosed lake to use our imaginations in order to accurately understand the concept.

In this closeup below, it can be seen that a ridge is coming in from the pattern field (on right)and abutting a ridge from the distal field. The distal ridge as seen aiming downwards ends and the next ridge is flowing in the same direction as a continuation of the distal ridge as it diverges marginally.

If the 3 meeting ridges are chosen as a meeting of 3 different fields and its center is the triradial point (fbi delta) this is incorrect as there is actually only a meeting of the distal and pattern fields.

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Right_16

The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition! - Page 2 Right_16

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