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Ellsworth Kelly: Black/Yellow (1972)
What type of polygons can you see inthis painting?
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Ellsworth Kelly: Black/Yellow (1972)
I can see two triangles and a yellowquadrilateral called isosceles trapezium
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Frank Stella: "Ossipee from the Eccentric Polygons Series#99"1974
Do you Know the name of this polygon?
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Frank Stella: "Ossipee from the Eccentric Polygons Series#99"1974
This polygon is a REGULAR PENTAGON
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Frank Stella: litografas
And now, do you know their names?
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Frank Stella: litografas A SQUARE, AN HEXAGON, AN OCTOGON
AND A DECAGON
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Josef Albers
COULD YOU DESCRIBE THIS PAINTING?
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Josef Albers
I CAN SEE FOUR SQUARES PAINTED WITHDIFFERENT COLORS. The smallest square isyellow and the biggest is brown. The smallestsquares are inside the biggest square.
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James Turrell: Raemar
What type of quadrilateral is thisshape?
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James Turrell: Raemar
This shape is a QUADRILATERAL, but it is alsoa PARALLELOGRAM and a RECTANGLE too.
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Donald Judd: Untitled
And This shape?
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Donald Judd: Untitled
It is a RHOMBOID
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Ellsworth Kelly: Red Curve in Relief. (2009)
HELLO, MY NAME IS.
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Ellsworth Kelly: Red Curve in Relief. (2009)
HELLO, MY NAME IS:
RECTANGLE TRAPEZIUM (UK)
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Ellsworth Kelly: Lake I. (1982)
I am a very common quadrilateral, I havent
got any parallel sides.
May I introduce my quadrilateral family?
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QUADRILATERALS PARALLELOGRAMS
(Both pairs of opposite sides areparallel)
SQUARES
RECTANGLES
RHOMBUS
RHOMBOIDS
TRAPEZIUMS (Two parallel sides and two non-parallel)
OTHER QUADRILATERALS
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Alexander Rodchenko: Esfera de color y Crculo. 1918
Whats the difference between a
circle and a circumference?
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Alexander Rodchenko
Could you describe the relative position of circles and
straight lines in this painting?
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Alexander Rodchenko
We can see external and secant lines.
(The external line does not touch the circumference, the secant cuts the
circumference at two points).
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Duchamp: Rueda de Bicicleta. (1913)
Could you point outor enumerate some
elements of thecircumference?
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Duchamp: Rueda de Bicicleta. (1913)
Radius, Diameter,Chord, Centre,
Segment Circular.
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Alexander Rodchenko: Escalera
What type of straight lines are
these?
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Alexander Rodchenko: Escalera
They are PARALLEL lines
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Piet Mondrian: Composicin con amarillo, azul y rojo.(1942)
And these other lines?
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Piet Mondrian: Composicin con amarillo, azul y rojo.(1942)
PERPENDICULAR lines
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Theo Van Doesburg: Counter- Composition XVI indissonances. 1925
Doesburg and Mondrian were friends for years, but in 1924 they broke theirfriendship. The exact reason for this split has been a point of contention among
art historians; usually the divergent ideas about the directions of the lines in the
paintings have been named as the primary reason: Mondrian never
accepted diagonals, whereas Doesburg insisted on the diagonal's
dynamic aspects, and indeed featured it in his art.
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Ellsworth Kelly: Two Panels. (1968)
This is a TWO-DIMENSION painting, BUTwe have the impression we are watching a.................. Shape, that is a
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Ellsworth Kelly: Two Panels. (1968)
This is a TWO-DIMENSION painting, BUTwe have the impression we are watching aTHREE-DIMENSION Shape, that is a SOLID
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Tony Smith: Die. (1962)
Here we have a big POLYHEDRON,
Could you tell us its name and
describe it a little?
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Tony Smith: Die. (1962)
It is a Regular POLYHEDRON. Its name isCUBE. A cube is a polyhedron with six
faces that are perpendicular to one
another, and with all its edges equals.
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Sol Lewitt: Forms derived from a cube
Again, we are watching cubes, but this time both have
lost a corner. They are truncated polyhedra.
Could you named the missing polyhedra?
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Sol Lewitt: Forms derived from a cube
On the right-hand side cube there is a smaller cube
missing and on the left-hand side cube a pyramid.
Are you sure they are truncated polyhedra?
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James Turrell: Raethro Pink. (1968)
What type of Polyhedra are these works of art?
James Turrell
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James Turrell: Raethro Pink. (1968)
They are pyramids, square Pyramids.
The base is a square and the lateral sides are isosceles
triangles.
James Turrell
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Donald Judd: Untitle. (1989)
These polyhedra are called .There is also another solid in these pictures, canyou see it?
do you know its name?
Donald Judd: Untitled. (1963)
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Donald Judd: Untitle. (1989)
These polyhedra are calledCUBOIDS(0R QUADRANGULAR PRISM)
We can also see a Cylinder, and empty cylinder
Donald Judd: Untitled. (1963)
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Robert Morris: Seven plywood structures painted grey.(1964)
As you can see, this Morris work use
different kind of CUBOIDS
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Maurits Cornelis Escher: Reptiles
Could you describe this well-known painting byEscher from the mathematical point of view?
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Maurits Cornelis Escher: Reptiles
Escher uses three important mathematical ideas in this painting:Two-dimension world (a flat world)
Three-dimension world
Regular Polyhedra (Escher draws a dodecahedron)
Do you know anymore regular polyhedra?
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A regular polyhedron must meet two criteria:1) Its faces are identical regular polygons.
2) The same number of faces meet at each of the
polyhedrons vertices.
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Maurits Cornelis Escher:Hand with Reflecting Globe
Here you can see another kind of Solid: It is not a
Polyhedron because its form implies a curved surface.
Could you tell us its name?
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Maurits Cornelis Escher:Hand with Reflecting Globe
It is a SPHERE, OF COURSE
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Parmigianino: Self-Portrait in a Convex mirror (1523-24)
Parmigianino used the same technique asEscher to paint his self-portrait. His image
comes from a spherical mirror.
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Anish Kapoor:Untitle. Creation
We can say this solid is a ..
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Anish Kapoor:Untitle. Creation
We can say this solid is a hemisphere
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Anish Kapoor:Memory. (2008)
Imagine this big globe made of steel were the earth.
Could you tell us the name of the curved lines around
its surface?
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Anish Kapoor:Memory. (2008)
Parallels and Meridians. They are related to Latitude
and Longitude.
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Anthony McCall: Breath II. (2004)
Anthony McCall: Between You and I. (2009)
Are these light solids pyramids?
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Anthony McCall: Breath II. (2004)
Anthony McCall: Between You and I. (2009)
No, they are CONES, they bases
aren't polygons, but circles.
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Nancy Holt: Sun Tunnels. (1973-1976)
Look at this Land art work and tell us
the name of the solids you see
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Nancy Holt: Sun Tunnels. (1973-1976)
Four CYLINDERS. A cylinder is a geometric solid boundedby two identical circles, called bases, and a curved lateral face.
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Nancy Holt: Sun Tunnels. (1973-76)
Now, look at the light
effects. Could you see twocircumferences with a common
tangent?
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Robert Smithson: Spiral - jetty . (1970)
As you can see, the name of this Land Art work is Spiral-jetty.
Here the author uses the SPIRAL form to express the
differences between human and nature activity.
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To Conclude: A piece of advice Dont
forget what you have seen
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LUIS M. RODRGUEZ MARTN
Mathematics DEPARTMENTIES ALBAYZNJANUARY 2011
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