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

Patti wrote:I just don't understand why you ignore the triangular shape and want to make a Y into the only possible choice of triradius regardless of the fact that the reguirements call for about 120 degrees and a minimum of 90 degrees.

You pointed out that the inside of an equilateral triangle was 60 degrees. Kiwi's is less than 60 degrees! So if the inside angle is 60 degrees when speaking of 120 degree angles, the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees. Kiwi's measures in the mid fifties.

Lynn wrote:

Martijn (admin) wrote:But that certainly doesn't mean that they say that there are 'only' 2 types of triradii - as suggested by Patti and adopted by you.

(1) I have never said 'only two types'. I've said there are two types clearly described. In fact Henry gives us a 3rd type when he talks about diverging ridges.

I think Patti's idea is just an 'over-simplifiction', that is not helpful at all (because it includes elements of phantasy). Again, she is only using that 'idea' to continue her phantasies about how triangles develop... but her model doesn't work because she simply ignores what is going on outside her triangles.

(2) sorry - which idea are you talking about?

Patti wrote:

Lynn wrote:

Martijn (admin) wrote:But that certainly doesn't mean that they say that there are 'only' 2 types of triradii - as suggested by Patti and adopted by you.

I have never said 'only two types'. I've said there are two types clearly described. In fact Henry gives us a 3rd type when he talks about diverging ridges.

I think the 'diverging ridges' is simply the open cornered triangle shape.

Lynn wrote:

Patti wrote:I just don't understand why you ignore the triangular shape and want to make a Y into the only possible choice of triradius regardless of the fact that the reguirements call for about 120 degrees and a minimum of 90 degrees.

You pointed out that the inside of an equilateral triangle was 60 degrees. Kiwi's is less than 60 degrees! So if the inside angle is 60 degrees when speaking of 120 degree angles, the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees. Kiwi's measures in the mid fifties.

Patti I'm not understanding this at all!
1) Kiwi's print does not have a triangle (in the sense of C&M delta of perfectly formed little triangles)
2) "if the inside angle is 60 degrees when speaking of 120 degree angles" ???
The angles inside an equilateral triangle are 60 degrees. The 120 degrees refers to the angles between the radiants of a 'perfectly formed' 'star' triradius.
3) "the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees." ????
It's impossible to have a triangle with an "outer" angle of 90 degrees! Or, if you mean a 90 degree angle inside the triangle, then the other two angles must add up to 90 degrees.
(or, have I completely misunderstood what you are saying?)

Lynn, I did not understand those details in Patti's comment either... but meanwhile I get blamed for ignoring the 'triangular shape' in the grooves... which all books only tell us to focuss on the ridges only.

( ... the angles again... )

Lynn wrote:

Patti wrote:I just don't understand why you ignore the triangular shape and want to make a Y into the only possible choice of triradius regardless of the fact that the reguirements call for about 120 degrees and a minimum of 90 degrees.

You pointed out that the inside of an equilateral triangle was 60 degrees. Kiwi's is less than 60 degrees! So if the inside angle is 60 degrees when speaking of 120 degree angles, the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees. Kiwi's measures in the mid fifties.

Patti I'm not understanding this at all!
1) Kiwi's print does not have a triangle (in the sense of C&M delta of perfectly formed little triangles)
2) "if the inside angle is 60 degrees when speaking of 120 degree angles" ???
The angles inside an equilateral triangle are 60 degrees. The 120 degrees refers to the angles between the radiants of a 'perfectly formed' 'star' triradius.
3) "the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees." ????
It's impossible to have a triangle with an "outer" angle of 90 degrees! Or, if you mean a 90 degree angle inside the triangle, then the other two angles must add up to 90 degrees.
(or, have I completely misunderstood what you are saying?)

Lynn wrote:

Patti wrote:

Lynn wrote:

Martijn (admin) wrote:But that certainly doesn't mean that they say that there are 'only' 2 types of triradii - as suggested by Patti and adopted by you.

I have never said 'only two types'. I've said there are two types clearly described. In fact Henry gives us a 3rd type when he talks about diverging ridges.

I think the 'diverging ridges' is simply the open cornered triangle shape.

Yes so do I. So that's a 3rd variant. It's not the same as C&M delta where there is a little triangle with ridges meeting at the angles.

Lynn wrote:Earlier in the discussion, I asked who first used the term 'triradius'.
I thought Galton used the word 'delta' but according to Chris C. Plato, Ralph M. Garruto, Blanka A. Schaumann in "Dermatoglyphics:science in transition, Volume 27, Issue 2"
(page 11)
Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

http://books.google.com/books?ei=8lW8TdefAcjQ4waR0-XnBQ&ct=result&id=ZaFsAAAAMAAJ&dq=henry+Classification+and+Use+of+Fingerprints+triradius&q=triradius#search_anchor

Lynn wrote:

Patti wrote:

Lynn wrote:

Martijn (admin) wrote:But that certainly doesn't mean that they say that there are 'only' 2 types of triradii - as suggested by Patti and adopted by you.

I have never said 'only two types'. I've said there are two types clearly described. In fact Henry gives us a 3rd type when he talks about diverging ridges.

I think the 'diverging ridges' is simply the open cornered triangle shape.

Yes so do I. So that's a 3rd variant. It's not the same as C&M delta where there is a little triangle with ridges meeting at the angles.

Lynn wrote:Earlier in the discussion, I asked who first used the term 'triradius'.
I thought Galton used the word 'delta' but according to Chris C. Plato, Ralph M. Garruto, Blanka A. Schaumann in "Dermatoglyphics:science in transition, Volume 27, Issue 2"
(page 11)
Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

http://books.google.com/books?ei=8lW8TdefAcjQ4waR0-XnBQ&ct=result&id=ZaFsAAAAMAAJ&dq=henry+Classification+and+Use+of+Fingerprints+triradius&q=triradius#search_anchor

Lynn wrote:Ok thanks Patti, I now understand what you are saying about angles of triangles, but I'm afraid I've lost the point of it? You're saying Kiwi's bifurcation is less than 90 degrees .... and what is less than 60 degrees?

Lynn wrote:Ok thanks Patti, I now understand what you are saying about angles of triangles, but I'm afraid I've lost the point of it? You're saying Kiwi's bifurcation is less than 90 degrees .... and what is less than 60 degrees?

Patti wrote:

Lynn wrote:

Patti wrote:I just don't understand why you ignore the triangular shape and want to make a Y into the only possible choice of triradius regardless of the fact that the reguirements call for about 120 degrees and a minimum of 90 degrees.

You pointed out that the inside of an equilateral triangle was 60 degrees. Kiwi's is less than 60 degrees! So if the inside angle is 60 degrees when speaking of 120 degree angles, the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees. Kiwi's measures in the mid fifties.

Patti I'm not understanding this at all!
1) Kiwi's print does not have a triangle (in the sense of C&M delta of perfectly formed little triangles)
2) "if the inside angle is 60 degrees when speaking of 120 degree angles" ???
The angles inside an equilateral triangle are 60 degrees. The 120 degrees refers to the angles between the radiants of a 'perfectly formed' 'star' triradius.
3) "the inside angle of a 90 degree measurement of a triangle's angle would be much less than 60 degrees." ????
It's impossible to have a triangle with an "outer" angle of 90 degrees! Or, if you mean a 90 degree angle inside the triangle, then the other two angles must add up to 90 degrees.
(or, have I completely misunderstood what you are saying?)

Re: 1) No the corners are not merged together, except for the top corner which is abutting. The proximal and marginal corners (or diverging ridges) do not touch.

Re: 2) The inside angles of an equilateral triangle with 3 ridges meeting is 120 degrees. The inside angle of an equilateral triangle with the meeting corners 120 degrees apart is 60 degrees.

Re: 3) You're right I did explain that in a confusing fashion. How about this?



A is at an inside angle of 90 degrees. This is the distance apart the branches of a bifurcation must be in order to qualify as a triradius.

Martijn (admin) wrote:

Lynn wrote:Ok thanks Patti, I now understand what you are saying about angles of triangles, but I'm afraid I've lost the point of it? You're saying Kiwi's bifurcation is less than 90 degrees .... and what is less than 60 degrees?

Lynn... are you sure?

Patti 'explained' regarding your second point at point 2:

"The inside angles of an equilateral triangle with 3 ridges meeting is 120 degrees. The inside angle of an equilateral triangle with the meeting corners 120 degrees apart is 60 degrees."

But I think her first sentence should have said mention 60 degrees, not 120 degrees.
And the second sentence... I can't make anything from that.

Can you???

Lynn wrote:

Martijn (admin) wrote:

Lynn wrote:Ok thanks Patti, I now understand what you are saying about angles of triangles, but I'm afraid I've lost the point of it? You're saying Kiwi's bifurcation is less than 90 degrees .... and what is less than 60 degrees?

Lynn... are you sure?

Patti 'explained' regarding your second point at point 2:

"The inside angles of an equilateral triangle with 3 ridges meeting is 120 degrees. The inside angle of an equilateral triangle with the meeting corners 120 degrees apart is 60 degrees."

But I think her first sentence should have said mention 60 degrees, not 120 degrees.
And the second sentence... I can't make anything from that.

Can you???

yes of course you're right Martijn, I was concentrating more on the diagrams to try and understand what Patti was saying. Yes it should be - the inside angles of an equilateral triangle are each 60 degrees.
I also didn't understand 'the meeting corners 120 degrees apart' hence I looked at the diagrams for clarification and I think Patti is referring to a line drawn from the angle of the triangle to the centre of the triangle - these lines meet at a point and are 120 degrees apart.
(is that what you were saying Patti? sorry your terminology about 'inside angles' seems to be referring to 2 different things, hence I was confused.)

Martijn (admin) wrote:

Lynn wrote:Earlier in the discussion, I asked who first used the term 'triradius'.
I thought Galton used the word 'delta' but according to Chris C. Plato, Ralph M. Garruto, Blanka A. Schaumann in "Dermatoglyphics:science in transition, Volume 27, Issue 2"
(page 11)
Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

http://books.google.com/books?ei=8lW8TdefAcjQ4waR0-XnBQ&ct=result&id=ZaFsAAAAMAAJ&dq=henry+Classification+and+Use+of+Fingerprints+triradius&q=triradius#search_anchor

Hi Lynn,

Thanks for mentiong that.
But is it true?

I have tried to check it at: http://www.galton.org/ (via search button in the upper left corner)

And it appears that the word triradius is not mentioned in any of Galton's books!

So, maybe we should read that comment of Garuto & Plato as: "In addition to introducing the term delta, ..."

Patti wrote:

Lynn wrote:Ok thanks Patti, I now understand what you are saying about angles of triangles, but I'm afraid I've lost the point of it? You're saying Kiwi's bifurcation is less than 90 degrees .... and what is less than 60 degrees?

Martijn's choice of a bifurcation on Kiwi's print as the triradius is wrong because the lower inside angle of the lower two branches are less than 90 degrees. They were measured in the mid 50s.

Patti, if you take a look at the angles between the upper two central ridges (on the right and left side of your 'yellow marked figure')... then you can see that the angle between those ridges is not very large.




But in Kiwihands´ fingerprint the exact size of the angle is very hard to establish, since the width of the ridge varies significantly.

However, the blue lines illustrate that my claim for a ´triradius´ ... really does not require any phantasy at all. Because the result of the angle measurement really depends on where you start measuring the angle of those ridges, and how the central line of the ridges is drawn!

And finally, my picture below also illustrates that there is no 'triangle' at all seen in the CENTRAL GROOVE, because at best it can be described as a 'quadrilateral' (which is an arow-like shaped polygon).


PS. The angle between the light blue lines in the downward pointing 'radiants' is exactly 100 degrees! I hope this helps you recognize how 'subjective' your arguments about your 2 phantasy-triangles and the bifurcation angle really are.

And that my claim for a 'triradius' (based on the arguments that I present earlier regarding the 'curving of the radiants') really is not 'deceiving' at all.

Patti wrote:I'll add to that from "Personal Idenfification" 1918 page 121 footnote:



The authors, either Wentworth or Wilder changed the name from Delta (Galton) to Triradius. This would then have to have been much prior to 1918 as they say it is at the time of writing widely accepted in the field.

Lynn wrote:

Martijn (admin) wrote:

Lynn wrote:Earlier in the discussion, I asked who first used the term 'triradius'.
I thought Galton used the word 'delta' but according to Chris C. Plato, Ralph M. Garruto, Blanka A. Schaumann in "Dermatoglyphics:science in transition, Volume 27, Issue 2"
(page 11)
Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

http://books.google.com/books?ei=8lW8TdefAcjQ4waR0-XnBQ&ct=result&id=ZaFsAAAAMAAJ&dq=henry+Classification+and+Use+of+Fingerprints+triradius&q=triradius#search_anchor

Hi Lynn,

Thanks for mentiong that.
But is it true?

I have tried to check it at: http://www.galton.org/ (via search button in the upper left corner)

And it appears that the word triradius is not mentioned in any of Galton's books!

So, maybe we should read that comment of Garuto & Plato as: "In addition to introducing the term delta, ..."

Yes Martijn, you're right! I can't find any mention of the word triradius, or tri-radius. Only delta.
Thanks for the links. It is interesting to read his explanation of the delta or triangular plot.
he talks about the inter-space. Once again this ties in with the idea that I am stubbornly holding onto (seems we can all be stubborn! ;-) about my original understanding of triradius.

http://galton.org/cgi-bin/searchImages/galton/search/books/fingerprint-directories/pages/fingerprint-directories_0065.htm

1) Galton's description is not like C&M illustrations of 'neat perfect little triangles' he describes it as " a small and rudely shaped triangle". Hence I guess the term 'triangular plot' as opposed to 'triangle'.

2) Which brings me back to what I said originally about my understanding of a triradius (and Patti has recently been saying - and today she posted one of Penrose examples of triradial area coloured in yellow to illustrate it.)

Martiin, would you agree that this could be described as a 'rudely shaped triangle' in an 'interspace' ?
The area I've coloured in black being the triradial area, the ridges that form its boundary being the triradius, the central point inside it being the triradial point.

If the ridges that form the boundary join up to an actual little triangle then they become C&M delta type triradius. Of course there might be ridges inside the black area that form the 'perfect star' triradius, then the triradius shifts to those ridges such as in Penrose example A.

I think that if we think of it like this, then it solves all the problems.

I know I keep harping on about it & Martijn so far hasn't been convinced, but that seemed to be because Martijn's definition of 'triangular plot' was based on the illustrations in C&M where the the ridges join to form perfect triangles. I had to concede that my version was not a perfect triangle. But now I see Galton's 'delta' isn't a perfect triangle, but a 'rudely shaped triangle' so I am trying again! What are your objections to it Martijn?

Hi Lynn,

Thanks for confirming that the info describe in the article by Garuto & Plato is not correct about Galton introducing the word 'triradius'. This shows again how confusing the scientific documents sometimes can be! Because, if you read the context properly than one can see that Garuto and Plato do not use the word 'delta' at all, to where they write 'triradius'... you should actually read 'delta' - and then it is just fine what they describe (just a formal mistake because they only use the word 'triradius').


Regarding your idea that you might be close at solving all problems, I don't think so - because you only jumped back to your old idea about the triradius (which only describe the 'triradial area').

And of course! => By reading Galton that old idea about the 'triradius' is confirmed.... because you old definition rigins directly from Galton's delta-concept! (I have described that earlier, I think you never thought about that while reading Galton's works).


Regarding Cummins & Midlo's 'triangular shape'... we know that it can sometimes be seen in a fingerprint; but that variant does not directly relate to Galton's little black triangles in his pictures.

Because Galton's little black triangles relate to the 'triradial area', which is illustrated by the fact that in many of those pictures he does not trace any ridges from those triangles at all. Galton describes that his 'deltas' always are present in loops and whorls (which perfectly makes sense if you recognize that his delta only relates to the triradial area!).

And again, we know that Cummins & Midlo's variant of the 'triangular plot' variant for the triradius is actually vary rare!

Do you now see the difference as well?


So, it is important to remind that Galton's delta concept got outdated! (Because it was only focussed on the triradial area - thought he has described all other important elements as well in his work, he did not describe an update for his delat definition).

And therefore your old concept for the triradius is outdated as well!!


Lynn, while reading anything about definitions etc.... it is very important to be very aware of the context where certain words are presented (Who is the author? When was it published? In what perspective?).

Because often the context is decisive for explain the meaning of the vocabulary used in the sentences.


Again, Galton is talking that delta that requires always to be present. While Cummins & Midlo talk about a 'triangular plot' (in the perspective of Galton's delta concept), but their 'triangular plot' is a triradius variant that is actually very rare (e.g. it is not seen in the 10 fingerprint examples that the present).

I hope you now see as well how confussing this materials really are?
And I hope this makes you recognize as well why I earlier started talking about the confusing, problematic aspects in Cummins & Midlo's approach (including e.g. the first sentence of the triradius definition + the title of figure 47).


MY CONCLUSION:

Sorry Lynn, I think you got lost in some details in Galton's work... and therefore you think that you have solved the problem. But you only stepped back by embracing your old definitions again, which origined from Galton's outdated work.



EDIT (2x):

PS. Regarding your question about the black shape that you painted in the picture:

"Martiin, would you agree that this could be described as a 'rudely shaped triangle' in an 'interspace'?"

No, because while Galton talked about a small rudimentary triangle that refered directly to the black triangles in his illustrations. But his black triangles are actually a bit larger than the area you painted in the picture: because they represent what we call the 'triradial area'... which is of course always present once in loops, and twice in whorls.

But Cummins & Midlo's 'triradial plot' is actually a little bit smaller than the area that you painted black!

My perception is confirmed by Patti's quote from Galton's work, which explicitely describes that Galton's delta refers to thel 'small area where the three folds':

Martijn (admin) wrote:
... and Galton's famous quote is found on page 63 in 'Fingerprint Directories':

"An Arch contains no delta, a Loop has one, and a Whorls has two."




So, Galton's word 'delta' can definitely not directly relate to the little rare 'triangular plots' as described and mentioned by Cummins & Midlo. Because that specific triradius-shape variant that Cummins & Midlo describes... does exist... but it is usually not seen at all (it is quite rare: I think it is seen in about 5% all fingerprints).