Wolfgang von Wersin
Encyclopedia
Wolfgang von Wersin is a Czech-born designer
, painter
, architect
and author
that developed his career in Germany
.
He studied architecture at the Technische Hochschule
in Munich
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
s he calls orthogons.
forms; however, he eventually developed a style free of any kind clear of influence (including rural
folk
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
, glass
, tableware
fabric
and wallpaper
.
Wolfgang Von Wersin's book about the Orthogons gives detailed information about how to construct and use a special set of 12 inter-related rectangles to create a design. They are similar to what Jay Hambidge
called dynamic rectangle
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
as well as information regarding dynamic symmetry and aesthetics
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
, the Sixton is 1: square root of 3
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
, painter
, architect
and author
that developed his career in Germany
.
He studied architecture at the Technische Hochschule
in Munich
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
s he calls orthogons.
forms; however, he eventually developed a style free of any kind clear of influence (including rural
folk
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
, glass
, tableware
fabric
and wallpaper
.
Wolfgang Von Wersin's book about the Orthogons gives detailed information about how to construct and use a special set of 12 inter-related rectangles to create a design. They are similar to what Jay Hambidge
called dynamic rectangle
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
as well as information regarding dynamic symmetry and aesthetics
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
, the Sixton is 1: square root of 3
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
, painter
, architect
and author
that developed his career in Germany
.
He studied architecture at the Technische Hochschule
in Munich
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
s he calls orthogons.
forms; however, he eventually developed a style free of any kind clear of influence (including rural
folk
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
, glass
, tableware
fabric
and wallpaper
.
Wolfgang Von Wersin's book about the Orthogons gives detailed information about how to construct and use a special set of 12 inter-related rectangles to create a design. They are similar to what Jay Hambidge
called dynamic rectangle
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
as well as information regarding dynamic symmetry and aesthetics
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
, the Sixton is 1: square root of 3
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
Designer
A designer is a person who designs. More formally, a designer is an agent that "specifies the structural properties of a design object". In practice, anyone who creates tangible or intangible objects, such as consumer products, processes, laws, games and graphics, is referred to as a...
, painter
Painting
Painting is the practice of applying paint, pigment, color or other medium to a surface . The application of the medium is commonly applied to the base with a brush but other objects can be used. In art, the term painting describes both the act and the result of the action. However, painting is...
, architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
and author
Writer
A writer is a person who produces literature, such as novels, short stories, plays, screenplays, poetry, or other literary art. Skilled writers are able to use language to portray ideas and images....
that developed his career in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
.
He studied architecture at the Technische Hochschule
Technische Hochschule
Technische Hochschule is what an Institute of Technology used to be called in German-speaking countries, as well as in the Netherlands, before most of them changed their name to Technische Universität or Technische Universiteit in the 1970s and in the...
in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s he calls orthogons.
Style
Wersin's early designs are characterized by East-AsianEast Asia
East Asia or Eastern Asia is a subregion of Asia that can be defined in either geographical or cultural terms...
forms; however, he eventually developed a style free of any kind clear of influence (including rural
Rural
Rural areas or the country or countryside are areas that are not urbanized, though when large areas are described, country towns and smaller cities will be included. They have a low population density, and typically much of the land is devoted to agriculture...
folk
Folk
The English word Folk is derived from a Germanic noun, *fulka meaning "people" or "army"...
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
Porcelain
Porcelain is a ceramic material made by heating raw materials, generally including clay in the form of kaolin, in a kiln to temperatures between and...
, glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
, tableware
Tableware
Tableware is the dishes or dishware , dinnerware , or china used for setting a table, serving food, and for dining. Tableware can be meant to include flatware and glassware...
fabric
Fabric
A fabric is a textile material, short for "textile fabric".Fabric may also refer to:*Fabric , the spatial and geometric configuration of elements within a rock*Fabric , a nightclub in London, England...
and wallpaper
Wallpaper
Wallpaper is a kind of material used to cover and decorate the interior walls of homes, offices, and other buildings; it is one aspect of interior decoration. It is usually sold in rolls and is put onto a wall using wallpaper paste...
.
Orthogon information
Jay Hambidge
Jay Hambidge was an American artist, born in Canada. He was a pupil at the Art Students' League in New York and of William Chase, and a thorough student of classical art. He conceived the idea that the study of arithmetic with the aid of geometrical designs was the foundation of the proportion and...
called dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
Sacred geometry
Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art...
as well as information regarding dynamic symmetry and aesthetics
Aesthetics
Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste, and with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste...
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
Square root of 2
The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.Geometrically the square root of 2 is the...
, the Sixton is 1: square root of 3
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property...
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
See also
Wolfgang von Wersin (Prague, 3 Dec 1882; Bad Ischl, 13 June 1976) is a Czech-born designerDesigner
A designer is a person who designs. More formally, a designer is an agent that "specifies the structural properties of a design object". In practice, anyone who creates tangible or intangible objects, such as consumer products, processes, laws, games and graphics, is referred to as a...
, painter
Painting
Painting is the practice of applying paint, pigment, color or other medium to a surface . The application of the medium is commonly applied to the base with a brush but other objects can be used. In art, the term painting describes both the act and the result of the action. However, painting is...
, architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
and author
Writer
A writer is a person who produces literature, such as novels, short stories, plays, screenplays, poetry, or other literary art. Skilled writers are able to use language to portray ideas and images....
that developed his career in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
.
He studied architecture at the Technische Hochschule
Technische Hochschule
Technische Hochschule is what an Institute of Technology used to be called in German-speaking countries, as well as in the Netherlands, before most of them changed their name to Technische Universität or Technische Universiteit in the 1970s and in the...
in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s he calls orthogons.
Style
Wersin's early designs are characterized by East-AsianEast Asia
East Asia or Eastern Asia is a subregion of Asia that can be defined in either geographical or cultural terms...
forms; however, he eventually developed a style free of any kind clear of influence (including rural
Rural
Rural areas or the country or countryside are areas that are not urbanized, though when large areas are described, country towns and smaller cities will be included. They have a low population density, and typically much of the land is devoted to agriculture...
folk
Folk
The English word Folk is derived from a Germanic noun, *fulka meaning "people" or "army"...
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
Porcelain
Porcelain is a ceramic material made by heating raw materials, generally including clay in the form of kaolin, in a kiln to temperatures between and...
, glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
, tableware
Tableware
Tableware is the dishes or dishware , dinnerware , or china used for setting a table, serving food, and for dining. Tableware can be meant to include flatware and glassware...
fabric
Fabric
A fabric is a textile material, short for "textile fabric".Fabric may also refer to:*Fabric , the spatial and geometric configuration of elements within a rock*Fabric , a nightclub in London, England...
and wallpaper
Wallpaper
Wallpaper is a kind of material used to cover and decorate the interior walls of homes, offices, and other buildings; it is one aspect of interior decoration. It is usually sold in rolls and is put onto a wall using wallpaper paste...
.
Orthogon information
Jay Hambidge
Jay Hambidge was an American artist, born in Canada. He was a pupil at the Art Students' League in New York and of William Chase, and a thorough student of classical art. He conceived the idea that the study of arithmetic with the aid of geometrical designs was the foundation of the proportion and...
called dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
Sacred geometry
Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art...
as well as information regarding dynamic symmetry and aesthetics
Aesthetics
Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste, and with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste...
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
Square root of 2
The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.Geometrically the square root of 2 is the...
, the Sixton is 1: square root of 3
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property...
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
See also
Wolfgang von Wersin (Prague, 3 Dec 1882; Bad Ischl, 13 June 1976) is a Czech-born designerDesigner
A designer is a person who designs. More formally, a designer is an agent that "specifies the structural properties of a design object". In practice, anyone who creates tangible or intangible objects, such as consumer products, processes, laws, games and graphics, is referred to as a...
, painter
Painting
Painting is the practice of applying paint, pigment, color or other medium to a surface . The application of the medium is commonly applied to the base with a brush but other objects can be used. In art, the term painting describes both the act and the result of the action. However, painting is...
, architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
and author
Writer
A writer is a person who produces literature, such as novels, short stories, plays, screenplays, poetry, or other literary art. Skilled writers are able to use language to portray ideas and images....
that developed his career in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
.
He studied architecture at the Technische Hochschule
Technische Hochschule
Technische Hochschule is what an Institute of Technology used to be called in German-speaking countries, as well as in the Netherlands, before most of them changed their name to Technische Universität or Technische Universiteit in the 1970s and in the...
in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
(1901–1904) and, in parallel (1902 to 1905), he also studied drawing and painting at the Lehr- und Versuch-Atelier für Angewandte und Freie Kunst ("Teaching and Experimental Atelier for Applied and Free Art"), a reform oriented art school in the same city. Then, from 1906 onwards, after he completed his military service, became a tutor there. His constant collaborator and eventual wife, the German printmaker and draughtswoman Herthe Sch?pp (1888–1971), met him as his pupil. In 1909 he began working as a designer for numerous firms, including the Behr furniture factory and the Meissen porcelain manufacturers. In 1929, he assumed the directorship of the Neue Sammlung established in Munich in 1925, the department for artisan art at the National Museum – and remained there until his illegal dismissal by the national socialists in 1934.
In 1956 he wrote The Book of Rectangles, Spatial Law and Gestures of The Orthogons Described, in which he describes a set of 12 dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s he calls orthogons.
Style
Wersin's early designs are characterized by East-AsianEast Asia
East Asia or Eastern Asia is a subregion of Asia that can be defined in either geographical or cultural terms...
forms; however, he eventually developed a style free of any kind clear of influence (including rural
Rural
Rural areas or the country or countryside are areas that are not urbanized, though when large areas are described, country towns and smaller cities will be included. They have a low population density, and typically much of the land is devoted to agriculture...
folk
Folk
The English word Folk is derived from a Germanic noun, *fulka meaning "people" or "army"...
art) and achieved a timelessly classical style of great objectivity, revealed above all in articles for everyday use, such as porcelain
Porcelain
Porcelain is a ceramic material made by heating raw materials, generally including clay in the form of kaolin, in a kiln to temperatures between and...
, glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
, tableware
Tableware
Tableware is the dishes or dishware , dinnerware , or china used for setting a table, serving food, and for dining. Tableware can be meant to include flatware and glassware...
fabric
Fabric
A fabric is a textile material, short for "textile fabric".Fabric may also refer to:*Fabric , the spatial and geometric configuration of elements within a rock*Fabric , a nightclub in London, England...
and wallpaper
Wallpaper
Wallpaper is a kind of material used to cover and decorate the interior walls of homes, offices, and other buildings; it is one aspect of interior decoration. It is usually sold in rolls and is put onto a wall using wallpaper paste...
.
Orthogon information
Jay Hambidge
Jay Hambidge was an American artist, born in Canada. He was a pupil at the Art Students' League in New York and of William Chase, and a thorough student of classical art. He conceived the idea that the study of arithmetic with the aid of geometrical designs was the foundation of the proportion and...
called dynamic rectangle
Dynamic rectangle
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry, which in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books...
s. The set of 12 Orthogons is determined by expanding a square through a series of arcs and cross-points until another square is formed on top, an exact duplication of the original square.
Wersin also explains in the book how Orthogons can be detected and used in architecture, ceramics, furniture and works of art.
The value of using Orthogons is explained in an excerpt that includes an extraordinary copy of text from the year 1558 (Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
). Diagrams of seven of the 12 orthogons are accompanied by a passage from the 1558 text cautioning that careful attention be given as the “ancient” architects believed “nothing excels these proportions” as “a thing of the purest abstraction.”
One of the orthogons, the hemidiagon, is apparent in the designs of synagogues in ancient Galilee. http://198.62.75.1/www1/ofm/sbf/Books/LA41/LA41449Milson_SynagoguesV.pdf Mathematical ratios and another source for the term Orthogon: http://wfgw.diemorgengab.at/WfGWformel.htm
A well-known Orthogon, the Auron (golden rectangle), has been employed to create a range of designs from posters and chapels (Mies van der Rohe), to chairs. and glassware
The Auron is related to musical harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
, in that the golden ratio is among the most dissonant musical intervals, and is also is included in discussions on sacred architecture and sacred geometry
Sacred geometry
Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art...
as well as information regarding dynamic symmetry and aesthetics
Aesthetics
Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste, and with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste...
.
According to Von Wersin, "The Orthogons are without exception root figures and are all irrational numbers. The calculations for measure relations of the Orthogons are based, without exception, on the Pythagorean doctrine." Examples of these root figure relations are: the Diagon relation is 1: square root of 2
Square root of 2
The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.Geometrically the square root of 2 is the...
, the Sixton is 1: square root of 3
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property...
and the Doppelquadrat is 1: square root of 4.
Mathematical ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Ratios for all twelve Orthogons:
http://wfgw.diemorgengab.at/WfGWformel.htm
Quadrat 1:1 – Hemidiagon 1:1.118 – Trion 1:1.154 – Quadriagon 1:1.207 – Biauron 1:1.236 – Penton 1:1.376 –
Diagon 1:1.414 – Bipenton 1:1.46 – Hemiolion 1:1.5 – Auron 1:1.618 – Sixton 1:1.732 – Doppelquadrat 1:2
See also
- AestheticsAestheticsAesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste, and with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste...
- Auron
- Golden rectangle
- Golden section
- Phi (letter)Phi (letter)Phi , pronounced or sometimes in English, and in modern Greek, is the 21st letter of the Greek alphabet. In modern Greek, it represents , a voiceless labiodental fricative. In Ancient Greek it represented , an aspirated voiceless bilabial plosive...
- Logarithmic spiralLogarithmic spiralA logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous...
- Fibonacci numberFibonacci numberIn mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
- Sacred architecture
- Sacred artSacred artSacred art is imagery intended to uplift the mind to the spiritual. Sacred art involves the ritual and cultic practices and practical and operative aspects of the path of the spiritual realization within the bosom of the tradition in question....
- Sacred geometrySacred geometrySacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art...
- Dynamic symmetry
- Giorgio MorandiGiorgio MorandiGiorgio Morandi was an Italian painter and printmaker who specialized in still life. His paintings are noted for their tonal subtlety in depicting apparently simple subjects, which were limited mainly to vases, bottles, bowls, flowers, and landscapes.-Biography:Giorgio Morandi was born in Bologna...
- Georges BraqueGeorges BraqueGeorges Braque[p] was a major 20th century French painter and sculptor who, along with Pablo Picasso, developed the art style known as Cubism.-Early Life:...
- Vitruvian manVitruvian ManThe Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci circa 1487. It is accompanied by notes based on the work of the famed architect, Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and...
- De ArchitecturaDe architectura' is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects...
- Square root of 2Square root of 2The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property.Geometrically the square root of 2 is the...
- Square root of 3Square root of 3The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property...
- Square root of 4
- Square root of 5
