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Niels Just Rasmussen




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PostPosted: Sun 18 Dec, 2016 10:28 am    Post subject:         Reply with quote

Peter Johnsson wrote:
The abbey of Fontenay was built by Saint Bernard of Clairvaux, who was deeply involved with the founding of the order of the Poor Fellow-Soldiers of Christ and the Temple of Solomon (the Templars).
The Fontanay abbey still exists with many of its original buildings still intact. The monks of this abbey were among other things known for their iron work. A smithy survives where the (one of?) oldest surviving water powered hammers is situated. The hammer was powered from the overflow of water from the fish pond. The smithy is huge: like sizeable church. There is only one black smith hearth surviving, however. Either there were more hearths originally, that have later been removed, or there ere other activities in the smithy that did not require heating of iron. A favourite fantasy of mine is naturally that they forged swords for the crusaders in this smithy, but there is no evidence for this being the case.

The cistecians were well known for their deep interest in geometry.
St Bernard famously said: "No decoration, only proportion" about how churches should be built.

When we take a closer look at the proportions of the abbey church of Fontenay it seems that its plan conforms to a simple geometric lay out.
(It should be noted that my analysis below is simply made from published plans of the abbey church, and therefore at best a suggestion.)

12th century swords have a likeness in the severe but sublime aesthetics of ecclesiastic buildings of the same period. The wide guards and the short grips undeniably have something romanesque or early gothic about them.They also show the same commensurable proportions of contemporary church architecture, combining simple geometric relations and modular ratios.

Making an overlay of some swords over the plan of the abbey church of Fontenay makes for some striking correlations. This is naturally not proof of anything, but perhaps something to reflect on at least.


The iron works of Fontenay makes it theoretically possible that they could produce gifts such as swords to benefactors of their order - such of Archbishop Eskil OR later members of the Hvide family like Archbishop Absalon or even King Valdemar the Great.

I found this info in an older book on Cistercian architecture:
Sharpe, Edmund (1874)
The Architecture of the Cistercians (p. 11-14)
.
Source: https://archive.org/details/architectureofci00shar

Of the general buildings, the church was, of course, the most important.
1) They were all dedicated to the blessed Virgin.
2) They were also all built after the form of the cross :
"Omnes ecclesiæ ordinis nostri in honorem Beatæ Mariæ dedicatæ sunt, et fere in modum crucis constructæ,
instar Ecclesiæ Cisterciensis omnium matris
."

The Choir was invariably short, seldom containing more than two compartments in length beyond the crossing ; and if that part of the plan of one of these early Cistercian churches which represents the choir, the transepts, and the nave, exclusive of chapels and side aisles, be tinted with a slight shade to distinguish it from the rest, it will be found to depict very exactly the form of a true Latin cross.
The east end was usually square, and not terminated with an apse; showing a marked departure from the manner in which churches of this date on the Continent were usually finished towards the east. Towards the close of the Xllth Century, however, the prevailing fashion of the times was introduced also into some of the churches of this Order, and the apse, with its accompanying chapels, applied to the east end.
The Transepts had no aisles, but invariably two or three chapels on their east sides, completely separated from one another by partition walls in the earlier examples. Each of these chapels had its altar and its piscina. In most of the ruined abbeys of this Order the site of these altars is apparent; and at Jervaulx Abbey, in Yorkshire, two of the altar stones remain in situ.

In many of the Cistercian churches we find a portico or narthex extending across the whole of the west end of the church. It had no great width, and was generally roofed as a lean-to against the west wall, and covered the west doorway,
as at Fountains and Byland ; but in some it was vaulted, as at Maulbronn and Pontigny. Its use is not very obvious.

We find no lofty towers in Cistercian churches, except such as were built after the rules of the Order became relaxed, as at Fountains and Furness, where towers were added in both cases towards the close of the Rectilinear Period : they were, in fact, expressly forbidden in the General Chapter of 1134.
"Cap. II. —De turribus ad Campanas.
Turres lupideæ ad campanas non fiant, nec ligneæ altitudinis immoderatæ, quæ ordinis dedeceant simplicitatem
.”

The Cistercians absolutely prohibited the carving or representation of the human form in their buildings, and give a reason for it which deserves consideration even at the present day.
"Cap. XX. —De sculpturis, et picturis, et cruce lignea.
Sculpturæ vel picturæ in ecclesiis nostris seu in officinis aliquibus Monasterii ne fiant interdicimus quia dum talibus intonditur,
utilitas bonæ meditationis vel disciplina religiosæ gravitatis sæpe negligitur; cruces tamen pictas, quæ sunt ligneæ,
habemus
.”

Furthermore no pictures were allowed - except the saviour - and neither were glass stained windows (unless it was already there in a monastery, they took over from a previous owner). Only kings and bishops could be buried in the church itself.

The Cistercians were amongst the first to employ and to utilize the pointed arch in their arches of construction, whilst their arches of decoration remained circular. There is not one of the conventual churches of the Xllth Century
given in the list at pages 27 and 28, in which this rule, to which I have so frequently called attention, was not observed.
...etc etc.


So clearly a strong aesthetic is with the order from the very beginning - it is highly likely that this aesthetic is also geometric (and not only for the resulting visual effect).


Last edited by Niels Just Rasmussen on Mon 19 Dec, 2016 1:00 pm; edited 2 times in total
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Peter Johnsson




PostPosted: Mon 19 Dec, 2016 12:49 am    Post subject:         Reply with quote

Mark: the last version of the analysis of the Morat sword is really elegant. I like way you reduced the number of components and how the root2 cut defines several important elements at the same time.

Niels: Thank you for posting further on cistercian architecture and aesthetic philosophy. This is a vast topic that I think would offer material that might well prove valuable for the study of swords.

I am sorry if I caused some misunderstanding in my post on the abbey church of Fontenay. None of the swords that share proportions with this church is the Søborg sword. They are other swords that I have come across in my studies. They are all of the same general type and share some similarities, but since they all have different dimensions, it is easily to miss the fact that many of their proportions have almost exactly the same ratios.

A further note of clarification:
I have been using the word commensurable to describe the way all parts of the swords are set in proportions that meet a single overall geometric structure.
Commensurability is sometimes understood as parts that relate to each other in ratios that are described by whole number integers (5/8, 3/4 and so on).
When I say that all elements of a design are Commensurable, I mean to say that all parts are measurable or comparable within a coherent geometric structure, even though some laments of the design cannot be described by natural integers since the geometry often result in cuts that create ratios involving irrational numbers.

Geometry can define proportions that are whole number divisions of a unit, but it is also capable of defining proportions that involve irrational numbers, like root numbers and the golden section. Before more advanced mathematical calculations were developed, geometric construction was the only way to construct such ratios in physical form. Imagine the power you wield by proper knowledge of the use of the geometers tools. You can divide any length in exactly even sections, or you can construct a shapes that involve both the rational and the irrational at the same time.
Consider for example the circle that express the natural numbers in its diameter and at the same time to irrational number Pi in its circumference, or the square that express the natural numbers in its side and at the same time the irrational number root2 in its diagonal. Irrational numbers cannot be expressed as a ratio of integers (i.e. 3/4). Instead they are an infinite series of decimals that do not repeat themselves (Pi = 3.14159265359....., the golden section Phi = 1.618033988749895…) . The kind of mathematics that work with such numbers did not exist in the medieval period. But the master artisans could still construct forms that expressed this mystical nature with the compass and the straight edge. That is an awesome power.

The play between rational and irrational numbers is a strong feature of geometric design and I personally have a feeling this was appreciated as beautiful and important by medieval artisans. I have no quote to prove this. It is simply a powerful impression after having worked according to these principles in analysing originals and designing my own work these past six years.

So when I say that the proportions of the sword are commensurable to the overall geometric structure, I intend to say that *all* important design features of the sword relates to the structure in a way that is directly defined by simple geometric cuts, regardless if the ratios created are based on rational or irrational numbers in a way that no part is left hanging, protruding or is left undefined. All parts are defined simultaneously both in proportion and in exact position to the overall structure.

If a design is developed by the use of modular units, there can also be commensurability, but under a less strict rule.You can always add or subtract a unit without having to worry of breaking any overall pattern. Exact position in the overall is also of little concern. Modular design is therefore a much more free and easy set of rules to follow.
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Peter Johnsson




PostPosted: Mon 19 Dec, 2016 4:08 am    Post subject:         Reply with quote

As part of the exhibition "The Sword - Form & Thought" at the Deutsches Klingenmuseum, I made a video about the geometry of sword design.
It is an introduction to symbolic significance and some basic geometry constructions that you regularly come across as elements of sword design. I also show some examples of actual designs of swords that were part of the exhibition.

The video is available on YouTube.
Please follow this link if you are interested:

https://www.youtube.com/watch?v=FiSoLMx3v0I

It is a bit long and slow unless you are into the mood of some contemplative music and geometry.
:-)
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Niels Just Rasmussen




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PostPosted: Mon 19 Dec, 2016 1:16 pm    Post subject:         Reply with quote

Other than Fontenay it seems there is conclusive evidence for iron works from the Cistercian Bordesley Abbey in Worcestershire.
The Abbey was founded in 1136 and the some of the timber from the iron works structure is dated 1174-1175 - a metalworking mill with millpoond, a workshop/smithy with two hearths, has been found.
It burned down during the 1180's or 1190's but was rebuild!

Source:
Lucas, Adam (2006)
Wind, Water, Work: Ancient And Medieval Milling Technology
page 272-273.

Also from Scandinavia we know that the Cistercian Sorø Abbey (founded on Sjælland by Bishop Absalon in 1161) had a "grangia" (grange for lay brothers) quite far away in Halland, where they extracted salt, iron ore and timer.

Source
France, James (2012)
Separate but Equal: Cistercian Lay Brothers 1120-1350
Page 117-121.


Last edited by Niels Just Rasmussen on Mon 02 Jan, 2017 8:01 am; edited 1 time in total
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Mark Lewis




PostPosted: Wed 21 Dec, 2016 2:52 pm    Post subject:         Reply with quote

Peter Johnsson wrote:
Mark: the last version of the analysis of the Morat sword is really elegant. I like way you reduced the number of components and how the root2 cut defines several important elements at the same time.

I was very pleased at how well that one finally worked out. Happy

Peter Johnsson wrote:
When I say that all elements of a design are Commensurable, I mean to say that all parts are measurable or comparable within a coherent geometric structure, even though some laments of the design cannot be described by natural integers since the geometry often result in cuts that create ratios involving irrational numbers.

Thanks for this clarification, in my posts I was using the term in the more limited sense of whole number ratios only.

Next I have been comparing a few swords with type B1 pommels, and some possible common elements appear in how the width of the pommel, blade and cross are related...

The swords are respectively from Padasjoki, Finland, Oakeshott's XI.1 in Records, inscribed NISOMEFECIT, and a sword in Stade inscribed BENNOMEFECIT. The first sword has lost a little from the tip of it's blade, but I've drawn it with a conjectural type 2 structure that allows for about another centimeter of length... the second is lacking precise measurements and quality photos. If I have identified the proportions of the hilt correctly, a triple ratio of 3:5:19 is formed between hilt length, cross width, and blade length.

The accuracy of my diagram for the Stade sword can be checked against the published measurements and deviations seem to be only a matter of millimeters. I've posted about this sword in the past, because of it's interesting inscription: http://myArmoury.com/talk/viewtopic.php?t=31165&highlight=



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Peter Johnsson




PostPosted: Sun 25 Dec, 2016 3:00 am    Post subject:         Reply with quote

Mark, I think it would be interesting to do an experiment.

I´d like to compare the results you can reach depending on point of departure in the analysis.
If we could find a sword where you have access to information on its dimensions that has been published in print or online, that I myself have made a direct tracing and documentation of, we could both show the result of our analysis.

The devil is in the details, as we all know.

We could see what similarities there might be or if there are any fundamental differences.

The question is if we could find such a sword?
Ideally, it would be one that is fairly well published.
Do you have any suggestions?

A sword from the Wallace Collection?
Possibly one of the Castillion swords that is well known publicly, or one from the Alexandria Arsenal?
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Mark Lewis




PostPosted: Mon 26 Dec, 2016 9:54 am    Post subject:         Reply with quote

Hi Peter,
This is a great idea, I really hope we can find some candidates for comparison!

For the Wallace Collection, I have enough measurements to make an attempt at analyzing A459, A460, and A462 (Oakeshott's Xa.1, XV.1, and XV.7).

I don't have very much data for the swords from Castillon... maybe the swords in the Royal Armouries are a possibility?

Regarding swords from Alexandria, I have the measurements from three of Clive Thomas' articles (on the XVIIIc's, pear-shaped pommels, and Aristay inscriptions). Apart from those, again I think I have the most measurements from the Royal Armouries, or some of the swords in Philadelphia, and one other in the Khalili Collection.

What about some of the swords found in the Fyris River? A couple of those have been published in detail.
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Luka Borscak




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PostPosted: Mon 26 Dec, 2016 1:52 pm    Post subject:         Reply with quote

I would love to see analysis of A.459. Happy
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Peter Johnsson




PostPosted: Wed 28 Dec, 2016 2:26 am    Post subject:         Reply with quote

From the Wallace Collection, I suggest the A.457 instead.
Mark, if you make an analysis of this sword based on the dimensions & photos available online or from the catalogue, I can then show my analysis based on first hand documentation of this sword.

We can compare any similarities or discrepancies.

Interesting?
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Mark Lewis




PostPosted: Thu 29 Dec, 2016 6:18 am    Post subject:         Reply with quote

I would definitely like to do A457 (actually I had a diagram in progress already). Disadvantage with this one is I don't have many measurements on hand... the website and 1962 catalogue only give the length and width of the blade. If there is any more data that you are permitted to share, or if another forum member has any more details, it would be a big help!

Luka Borscak wrote:
I would love to see analysis of A.459. Happy

I'd like to have a look at this one too, and will post the results if they are interesting. Wink
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Anthony Rischard




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PostPosted: Thu 29 Dec, 2016 7:08 am    Post subject:         Reply with quote

Mark Lewis wrote:
I would definitely like to do A457 (actually I had a diagram in progress already). Disadvantage with this one is I don't have many measurements on hand... the website and 1962 catalogue only give the length and width of the blade. If there is any more data that you are permitted to share, or if another forum member has any more details, it would be a big help!


Hello Mark, hi Peter!

I started talking to Vincent on the dynamics end of things after I got my own copy of The Sword -Form and Thought in the spring and had decided to put the geometry adventure on hold for a bit - until I came across this discussion a few days ago. I started researching A457 yesterday and did find a bit more. An old issue of Gladius (2003) has a total length in David Edge's article.

Here's an excerpt from my personal file on A457 with what I have so far:

Bibliography:
* Mann, James G., Wallace Collection Catalogues: European Arms and Armour Volume II, London: The Wallace Collection 1962
* Norman, A. V. B., Wallace Collection Catalogues: European Arms and Armour Supplement, London: The Trustees of the Wallace Collection, 1986
* Edge, David, and Alan Williams. "Some early medieval swords in the Wallace Collection and elsewhere." Gladius 23.1 (2003): 191-209. (http://gladius.revistas.csic.es/index.php/gla...Article/50)
* Oakeshott, Ewart. The sword in the age of chivalry. Boydell Press, 1997, p.85

Stats:
* Blade Length: 822 mm (WC-web)
* Total Length: 953 mm (Gladius 23.1)
* Width: 51 mm (WC-web)
* Weight: 1195 g (WC-web)

I have already begun normalising the image from the WC website, as parallax has indeed slightly skewed the blade to hilt proportion, and the guard is off square. If (and it is a big "if) I have time to try my own interpretation in the next few days, I'll post it as well.

I wish you all a lovely end of year and loads of geometric surprises for 2017

Kind regards,

Anthony
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Mark Lewis




PostPosted: Thu 29 Dec, 2016 8:49 pm    Post subject:         Reply with quote

Anthony Rischard wrote:
I started researching A457 yesterday and did find a bit more. An old issue of Gladius (2003) has a total length in David Edge's article.

I have already begun normalising the image from the WC website, as parallax has indeed slightly skewed the blade to hilt proportion, and the guard is off square.

Thanks Anthony! Having the overall length definitely helps. I remember that article, but hadn't thought to check it.

I can see the same distortion that you mention in the full-length photo on the museum website... the photos in Records of the Medieval Sword and Arms and Armor of the Medieval Knight seem to be more true to the actual proportion.


Last edited by Mark Lewis on Fri 30 Dec, 2016 4:50 am; edited 1 time in total
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Anthony Rischard




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PostPosted: Thu 29 Dec, 2016 11:23 pm    Post subject:         Reply with quote

You're welcome Mark. I'm following this thread with great interest. And thank you for reminding me to go check my own bookshelf for better photos rather than stopping at the "official" museum photo. A little technology bias on my part.

I woke up this morning with a thought and a proposition for a follow up experiment with Peter Johnsson.

It seems to me that we have a rather unique opportunity with Peter to check a geometric interpretation not only among different interpreters, but also against the source - the original intent.

There's an old short story (Asimov if I remember correctly) where Shakespear is brought through time to a modern University and utterly fails a freshman course on Shakespearean literature... Modern interpretation being so far from the original intent as to be incomprehensible to the author of the works.

We can check our interpretations of medieval swords against each other to stimulate thought, debate theory and refine technique, but we cannot test these interpretations against the intent of the original designer of the sword. We simply cannot ask him if we "got it right".

Except that with Peter, we can...

If Peter can provide you - provide us, if I dare join the game at this very early stage of my exploration - with the silhouette (in photo or drawing) and the basic measurements for a sword that he has designed using his geometric techniques, the interpretations can then be compared to his original intent and construction geometry.

This could help to show how accurately the geometric analysis model, as it stands, can reconstruct the design intent and perhaps underline if and where it can be refined to facilitate this kind of reconstruction.

Just a thought.

A happy and safe New Years weekend to all!
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Peter Johnsson




PostPosted: Fri 30 Dec, 2016 2:50 am    Post subject:         Reply with quote

Anthony Rischard wrote:


...If Peter can provide you - provide us, if I dare join the game at this very early stage of my exploration - with the silhouette (in photo or drawing) and the basic measurements for a sword that he has designed using his geometric techniques, the interpretations can then be compared to his original intent and construction geometry.

This could help to show how accurately the geometric analysis model, as it stands, can reconstruct the design intent and perhaps underline if and where it can be refined to facilitate this kind of reconstruction.

Just a thought.

A happy and safe New Years weekend to all!


Anthony, this is a great idea!
Let´s play.
Anyone who finds this interesting is more than welcome to join. The more the merrier.
I will supply material for you to analyse and we can compare the results.

Stay tuned, it will take me a day or two to prepare the material. Perhaps we can start at the beginning of the new year.
:-)

In the mean time I am interested to see what you find with the A457.
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Paul Watson




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PostPosted: Fri 30 Dec, 2016 2:02 pm    Post subject:         Reply with quote

There's a certain broad bladed Type XVIII on or around Peter's workbench at the moment that I would like to see this applied to.
I do not love the bright sword for its sharpness, but that which it protects. (Faramir, The Two Towers)
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Peter Johnsson




PostPosted: Sun 01 Jan, 2017 1:41 pm    Post subject:         Reply with quote

Happy New Year everybody!

Here are three swords to analyse for your enjoyment.
All three are designs made by me, but made to look like tracings of original swords with some slight asymmetries and inexactness, just like the ones you will find on originals.

Dimensions for their full size are given in millimetres: Total length, blade length, blade width, guard width & height + pommel width & height.

No. I
Tot: 1175mm BL/BW: 966mm / 50mm GW/GH: 227mm / 8.5mm PH/PW: 52mm / 63mm

No.II
Tot: 1127mm BL/BW: 929mm / 56mm GW/GH: 155mm / 9.8mm PH/PW: 48mm / 59mm

No. III
Tot: 1080mm BL/BW: 949mm / 48mm GW/GH: 187mm / 9.5mm PH/PW: 34mm / 78.8mm

EDIT:

You will now also find each sword as a separate image in jpg format. These might be easier to work with.
-Thanks!

-Also, since the drawings are true to proportion, the information about dimension is actually not necessary. One of the key features of proportional design is that an object can be scaled to the dimensions you need. There are naturally limits to the degree of scaling you can do with a sword, of course. A long sword scaled so that the grip has to the size of a single hand sword, will look odd and have a very short blade.
You can adjust for this by changing one single element of the design, making the blade longer in proportion to the hilt (and in so dong, turning a long sword into a single hand sword), or making the pommel smaller (and that way turning a single hand sword into a long sword). That way the design of a long sword can be changed into that of a single hand arming sword, or an arming sword turned into a long sword.

-So, you can absolutely disregard the dimensions given and only work from the drawings. Remember they are made to have some irregularities just like you can expect actual swords will have. I think you will still be able to find the underlying geometric structures.

Good luck!



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Last edited by Peter Johnsson on Mon 02 Jan, 2017 3:36 am; edited 1 time in total
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Anthony Rischard




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PostPosted: Mon 02 Jan, 2017 3:05 am    Post subject:         Reply with quote

Happy New Year everyone!

Peter, thanks for getting this out so quickly. Beautiful pieces, by the way - very elegant. I am quite drawn to n° 3. A powerful design.

It will be very interesting to see the results.

I propose that anyone wanting to join in (I still hope to, time permitting) wait until January 15 to post their interpretations, allowing each interpreter to work "blind", and giving everyone a bit of time to get to it.

Comparison, discussion and refinement will surely follow!

Cheers!

www.forge-art.com | www.blackarmoury.com
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Mark Lewis




PostPosted: Mon 02 Jan, 2017 7:43 am    Post subject:         Reply with quote

Happy New Year!

My analysis of A457 is ready for "grading" - have to say that I found this one quite difficult, so I'm not feeling much confidence in what I've come up with. Very curious to know if any of what I found will survive scrutiny!

Based on the published measurements the hilt to blade ratio is very close to 3:19, so I tried to use the same type 2 structure as previous examples. Inscribing an eight-pointed star seemed to give a nice solution for the width of the blade, but I wasn't able to extend the construction to include the dimensions of the cross and pommel.



Switching to a type 1 structure seemed more promising with a very simple solution for the width of the cross at least, and not-so-simple constructions for the pommel and blade width.





Thanks for sharing your own designs, Peter! Looking forward to working on these... Sword number 3 really stands out for me as well, so I'm definitely going to start with that one. Happy


Last edited by Mark Lewis on Mon 02 Jan, 2017 3:29 pm; edited 2 times in total
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Peter Johnsson




PostPosted: Mon 02 Jan, 2017 8:08 am    Post subject:         Reply with quote

Thank you Mark!

This is interesting to see.
I will hold back from showing my results a few days, to see if anyone else might want to join the fun first.

And..
I think you can find a simpler way to define that blade width in the structure you have (the type I structure, where you use the inscribed pentagons).

EDIT: -No, sorry. My mistake. I thought your solution with the inscribed pentagram and the diagonal arcs were the same as another figure. It was not.
But double check if the proportions in the photo are true to the measurements. Something is off.
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Mark Lewis




PostPosted: Mon 02 Jan, 2017 1:44 pm    Post subject:         Reply with quote

Peter Johnsson wrote:
But double check if the proportions in the photo are true to the measurements. Something is off.

You're right, the closeup from the Wallace Collection website has the same distortion as their full length photo - looks like it's just a crop of the original image. The black and white photo seems to be a bit better...

The guidelines for the width of the blade, lower edge of the guard, and upper edge of the pommel are drawn to scale based on the available measurements. Which part seems particularly off? I have the least confidence in the shape of the pommel, particularly the lower arc. Worried

Edit: Replaced inaccurate photo in previous post with a better(?) one.
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