Category Archives: Geometry

Tempelhof Airport _ Statement III _ and a Thank You

Berlin’s Tempelhof Airport, famous for its use during the Berlin Airlift of 1948, has been preserved and converted into a public park,
virtually unchanged in its landscape from when it was a functional airport.
It is an amazing public resource and a rare expansiveness in an urban setting; it reminds me of a mini-version of the American Great Plains
with the unobstructed views, open sky and flat, flat, flatness.
This was quite a contrast to the drama of the Himalayas
and the decoction of crowdedness and chaos
I experienced throughout India.

Samuel Nigro, Berlin, Tempelhof, Great CircleSamuel Nigro, Berlin, Tempelhof, Great CircleSamuel Nigro, Berlin, Tempelhof, Great CircleSamuel Nigro, Berlin, Tempelhof, Great CircleSamuel Nigro, Berlin, Tempelhof, Great Circle

During my three months in Berlin, I took to riding my bike around Tempelhof Airport almost everyday, coasting over the gentle rise and fall of terrain, up and down the runways and around and around the grounds without touching the handlebars for long, extended periods, and this free flow wandering in wide open space helped spur on my thoughts for Statement III, a piece of writing
I promised to publish in a previous post when I arrived in Berlin from India, in June 2014. 

However, Statement III still eludes me.

Below are five rough drafts. The first four are links to previous posts on this blog:

1. How to break a stone – in five easy steps.

2.a) Love G.I.T. – part I
2.b) Love G.I.T. – part II

3. Heutegesternmorgenwelt – a series:

a) Bread, Granite and Heutegesternmorgenwelt
b) Heutegesternmorgenwelt Resolved (Three Birds of Different Orders)
c) To Walk, To Mime … (Heutegesternmorgenwelt REDUX)

4.a) Three Stones from Three Cities – part 1
4.b) Three Stones from Three Cities – part 2

and

The fifth is a new attempt and a product of my Tempelhof Airport bike riding:

5. The Great Circle (Statement III – a rough draft):

As a young boy, I often imagined a line extending perpendicular from my direction of travel, going all the way around the planet and coming back perpendicularly to my other side, creating a giant ring around the globe, a Great Circle in the parlance of geometry, and, by definition, always concentric with the earth. Part of the excitement was to imagine the ring in its entirety, and go further and imagine that this Great Circle was attached to me, was me, and would move effortlessly with me, around and around our planet, hugging the surface of the earth in whatever way I could imagine. What it saw, I saw – what it felt, I felt – what it experienced, I experienced the same.

I varied the properties of this line by imagining it as different fantasy materials of varying thicknesses and flexibilities – so, I determined when it remained ridged, ignoring all the complexity of the planet and sweeping out perfect arcs of perfect circles and shaving the globe to a perfect sphere; or, I would loosen it up so it moved over only a specific topology like the hard earth crust or then include other objects and mold itself around just animals, or just people, just trees, plants, insects, just homes, buildings, structures; or, I’d make it so thin, so malleable that it conformed to different degrees of detail, zipping over complicated surfaces, effortlessly, conforming to every nook and crag, every flake, scale and leaf, every pebble, glop and glump, tuft, tassel and clump, every marble or toy, every detail and deeper, deeper detail still, sometimes skimming over water, sometimes conforming to every ripple, sometimes hugging the land and descending to the bottom of every depression, every lake, ocean and stream, every pool, every puddle, every bowl of soup, every cup of hot chocolate, every glass half empty or glass half full. As a boy, I figured that in principle my line could even conform down to the microscopic level, and this made me dizzy, as did interior spaces – they were difficult to imagine, too. Nevertheless, even knowing this abstract geometry existed and as I played to maintain harmonious and fluid motion between my mind and The Great Circle, I imagined being everywhere, always, at the same time: a total impossibility, and fun while it lasted, because …

By the age of 12 or so, I forgot about this thought exercise, this fantasy, really, and moved on: life demanded it. Life got more complicated, thinking complex – strategic designs varied with more teachers, more rules, more guidance; more religion, more grist for agreement and quests for influence, more ideology, more ingredience. Yet, my ability for abstraction both grew and became more focused, more refined. I mean: ‘x’ taking the place of a number in an equation is quite abstract; the tangent of ‘x’ even more so. In short, life and school and communication got more specific in its content and demanding in the way one must, inevitably, engage – and thinking about what was in my immediate purlieu began to dominate.

This Great Circle, this thought experiment, represents a framework of wonder and inquiry of a young boy, a method of investigation, a mode of thinking about his surroundings, an epistemological stance, if you will. I am now using a different method that includes a visual and physical manipulation of material, which marries this curiosity of the boy with all that he was taught and with all that he experienced along with the specific theme of breaking and placing stone, its movement and action, their opposites and the many gradations in between – which now serves as my present framework of discovery and of wonder and inquiry.

With the highlighting of these 5 rough drafts of Statement III, I need to shift my attention
away from this blog and the Internet machine for a while
and devote more concentrated time and effort in other, deeper directions – specifically, toward the work I furthered in India,
Cairns – Shards – Pieces – and, as this work proceeds,
Statement III will inevitably evolve.

I’m not disappearing from this digital land but my intention is to not post on this blog for a while and … well … I’ll let you know what’s next. Its brewing.
Sign up for my newsletter, because then you will be sure
to stay current. 

Thank you for your readership.

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Filed under Art, Geology, Geometry, Sculpture, Story

my most nostalgic post so far …

Horoballs and Tsvietkova

Horoballs (note: all the spheres are tangent to the z-plane) and Anastasiia Tsvietkova

Anastasiia Tsvietkova – Hyperbolic Structures from Link Diagrams

Anastasiia Tsvietkova – Hyperbolic Structures from Link Diagrams

14 prime knots with 7 crossings

14 prime knots with 7 crossings

I lucky got the chance to go to the last Geometry and Topology Seminar at CUNY Graduate center on December 11th right before the holidays. It was a treat.

Anastasiia Tsvietkova of Louisiana State University presented her dissertation entitled Hyperbolic Structures from Link Diagrams.
Rooted in knot theory and geometric topology, she builds upon W. Thurston’s Hyperbolization Theorem,
which demonstrates that every link in a 3-sphere is

a torus link,
a satellite link
or a hyperbolic link

and these three categories are mutually exclusive. That just SOUNDS satisfying.

Her dissertation lays out an alternative way to compute the hyperbolic link in a 2-DIMENSIONAL PROJECTION.

That deserves a “WOW!”

I enjoyed the talk very much, even though much of the math was over my head.
The fact that the whole lecture only dealt with 3-dimensions made it easier.
I, at least, understood what was at stake and enjoyed following
the structure of the argument.
You can read her paper.

The bottom line:

The lecture got me to open my Knot Theory book and
revisit my drawings of hyperbolic paraboloidal shapes
from Calculus III,

because knot theory is fun and I enjoy calculus.

Hyperbolic Paraboloids from Calc III

Hyperbolic Paraboloids from Calc III

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Filed under Drawing, Featured ..., Featured Thinker, Geometry, Math

How to break a stone – in five easy steps.

1. Move your mind:

example:

• Is the breaking of stone (or any material or space, for that matter) catastrophic or transformational? How is the view of the break changed when – additionally or solely – labeled “creative,” or “purposeful,” or “random,” or “predictable,” or “warranted,” or “gratuitous,” or “liminal,” or “signified?” (… to list a few common viewpoints) What are the criteria to judge such a label?

• What is the level of tragedy that is depicted in a specific break; or is the depiction a revolution, a rupture, or a salvation – however necessary, temporary or unexpected? How mediated would these outcomes be?

• More generally, What is the characteristic of the conflict that sustains the action, allowing it to be carried out – or is it really about an emergence of cooperation among various forcings?

• How can an initial read of the basic forms and actions that I deal with be reconciled with the deep geologic time and the wide historic import of stone and be brought into an epistemological rather than just a phenomenological discussion – and, really, how can the seriousness of these questions include a comic and humorous framework because of the unique demands of the human psyche?

• How does one move beyond the break – and beyond the tragic, the revolutionary, the ruptured, or the saved; the label, the criteria, the judgment: and to what end? Is there even an end (!?) and, if so, how strategic is it?

2. Move your body:

           example:

.
3. Repeat steps 1 and 2until the right stone presents itself.

4. Repeat steps 1 and 2 with chosen stoneuntil the method becomes clear.

5. Break.

I’m currently on step 3.

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a new project brewing

Samuel Nigro Sculpture CardboardSamuel Nigro Sculpture Cardboard
This cardboard model is 88″ high with a 20 x 20″ footprint.
It represents the volume of granite, which weighs almost two tons,
that I will be working with very soon.

Stay tuned …

and join my mailing list for insider info:
http://eepurl.com/norTf

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The Two Smallest

Two Smallest Pieces, Samuel Nigro, Drawing

Two Smallest Piece, graphite on paper, 32 x 48 inches, 2012

Smallest Piece, Samuel Nigro, Drawing

Smallest Piece, graphite on paper, 32 x 48 inches, 2012

Second Smallest Piece, Samuel Nigro, Drawing

Second Smallest Piece, graphite on paper, 32 x 48 inches, 2012

Three more drawings from the Granite Wall Series. This time I used the two smallest pieces. Can you find them in the sculpture?

Granite Wall, Samuel Nigro, sculpture

Background: Granite Wall (back); 108 x 54 x 5”, 2005
Foreground: Two Ton – Obverse (back); 20 x 20 x 102”, 2005

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