Facharbeit Geometrie

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und Blau stammen von der Flagge der englischen Kolonien (,,Union Jack") ab. Blau steht für Wachsamkeit, Beharrlichkeit und Gerechtigkeit. Rot bedeutet Tapferkeit und Widerstandsfähigkeit. Die Farbe Weiß steht für Reinheit und Unschuld. (vgl. Fisher) 2.2. Die Geschichte der Flagge Zur Zeit der Unabhängigkeitsbewegung im 18. Jahrhundert entstanden in den 13 englischen Kolonien in Amerika verschiedene Revolutionsflaggen. Die Sons of Liberty war eine der ersten Gruppe in Nordamerika, die sich gegen das Mutterland Großbritannien wendete. Die Flagge dieser Gruppierung ist eine der bekanntesten, aus der die heutige US-Flagge hervorging. Sie bestand zunächst aus neun vertikalen roten und weißen Streifen (vgl. Abb.2). Die Anzahl der Streifen stand für die neun Kolonien, die gegen ein britisches Gesetz protestierten. Später bestand die Flagge aus 13 horizontalen roten und weißen Streifen (vgl. Abb.3). Während der Revolution wurde die ,,Grand Union Flag" (vgl.Abb.4). bedeutsamer, die zusätzlich den britischen Union Jack links oben in der Ecke enthielt. (vgl. Shalev 2018) Abb. 3: frühere Sons of Liberty Flagge Abb. 2: Spätere Sons of Liberty Flagge Nach einer umstrittenen Legende soll die Kriegerwitwe Betsy Ross im Jahr 1776 den Auftrag erhalten haben, die amerikanische Flagge zu nähen. Sie soll diesen Auftrag von George Washington, dem späteren ersten Präsidenten der Vereinigten Staaten, Robert Morris, einem Kolonisten und Gründervater der Vereinigten Staaten, und ihrem Onkel George Ross erhalten haben." Betsy's descendents claim that the three men requested her to create the depicted flag." (National Postal Museum) Abb. 4: Grand Union Flag Nach einer Resolution von 1777 sollte die Flagge 13 Streifen und 13 Sterne für die 13 Kolonien erhalten, welche die Unabhängigkeit von den Vereinigten Staaten im Jahr 1776 erklärt haben. Im Jahr 1818 beschloss der amerikanische Kongress die Anzahl der 13 Streifen nicht zu verändern, aber für jeden neuen Bundesstaat einen neuen Stern hinzuzufügen. (vgl. WDR1 2017, Shalev 2018) 4 3. Mathematische Berechnung der Flagge Die Form der Flagge entspricht einem Rechteck, dessen Flächeninhalt sich aus dem Produkt der Grundseite und der Höhe berechnet. Die Formel lautet: ARechteck = A * B. Um die Flächenberechnung der US-Amerikanischen Flagge zu vereinfachen, teile ich sie in drei Flächen auf. Fläche 1 Fläche 3 Fläche 2 Abb. 5: Flächen der US-amerikanischen Flagge Die erste Fläche beinhaltet die sechs unteren Streifen und ist in der Abbildung blau markiert. Der Flächeninhalt für den ersten Teil beträgt, ausgehend von den Bezeichnungen aus der Abbil- dung1: Aunten = (A − C) * B. Die weißen und roten Streifen der Fläche 1 sind jeweils gleichgroß. Der Flächeninhalt der Strei- fen berechnet sich jeweils durch die Formel: Arotz = 3L * B und Aweiß2 = 3L * B Die anderen sieben Streifen bilden die zweite Fläche, die ich in der Abbildung grün markiert habe. Für die roten Streifen dieser Fläche berechnet sich der Flächeninhalt durch die Formel: Arot1= 4F (B - D) und für die weißen Streifen durch die Formel: Aweiß1 = 3F * (B − D) Die blaue Ecke oben links bildet die dritte Fläche, die hier gelb markiert wurde. Der Inhalt dieser blauen Fläche abzüglich der Fläche der weißen Sterne berechnet sich mittels der Formel Ablau = C* D - Asterne. 5 3.1. Zwischenergebnis Als Zwischenergebnis sich für die Flächen der drei Farben: Für Rot: Arotges = 3L * B + 4L * (B - D) Für weiß: Aweißges Für Blau: Ablauges = CD - Asterne = 3L * B + 3L * (B − D) + Asterne 4. Flächenberechnung eines Pentagramms Die Sterne in der Flagge sind Pentagramme. Ein Pentagramm ist ein fünfeckiger Stern, der sich aus fünf gleich langen Linien zeichnen lässt. In dieser Arbeit habe ich zwei Möglichkeiten betrachtet, um die Formel für die Flächenberechnung eines Pentagramms herzuleiten. Die erste Möglichkeit besteht darin, die Fläche des inneren Fünfecks, in der Abbildung 6 rot dargestellt, zu berechnen und die Fläche der übrigen fünf Spitzen, also die in der Abbildung grün dargestellten Dreiecke, zu addieren. Die zweite Möglichkeit ergibt sich dadurch, dass ich die Fläche des großen Fünfecks, einem Pentagon, berechne, das sich aus einer Verbindung der äußeren Punkte des Pentagramms ergibt. Von dem Flächeninhalt des Pentagons sind dann die Flächen der fünf in der Abbildung 7 rot dargestellten Dreiecke zu subtrahieren, die nicht zum Pentagramm gehören. Ich habe mich für die zweite Möglichkeit entschieden, da es den Rechenweg verkürzt und einfacher ist. a a Abb. 6: Inneres Fünfeck a a 6 a Abb. 7: Die Dreiecke, die subtrahiert werden müssen, für den Flächeninhalt eines Pentagramms 4.1. Mathematische Herleitung des Flächeninhaltes des Pentagons 4.1.1. Erster Ansatz Mein erster Ansatz war es, das Fünfeck in drei Dreiecke zu unterteilen, um die Rechnung zu vereinfachen. Um den Flächeninhalt eines gleichschenkligen Dreiecks zu berechnen, benötigt man die Grundseite a und die Höhe h. a*h Die Formel lautet: Apreieck = Diese Größen a und h sind bei den Dreiecken R und B nicht gegeben. Daher habe ich nach einem anderen Ansatz gesucht. 4.1.2. Zweiter Ansatz Dreiect Abb. 8: Erster Ansatz Allerdings gilt immer noch die Formel Apreieck = a*h und die Werte für a und h sind unbekannt. In dieser Formel ist kein Wert für die Variablen gegeben, deswegen muss sie vereinfacht werden. D' Die jeweiligen Dreiecke können in zwei rechtwinklige Dreiecke aufgeteilt werden. Nach diesem Schritt kann man nun mit dem Tangens von 36° rechnen. Die 36° ergeben sich aus der 7 a 360 Das Fünfeck kann in fünf gleiche Dreiecke aufgeteilt werden. Die Summer der Winkel müssen 360° ergeben, deswegen kann der Winkel eines Dreiecks durch. = 72° berechnet werden (vgl. Abb.9). 5 Dreek R 720 720 36⁰° AP Dreieck B 36 ⁹0° Abb. 9: Zweiter Ansatz Halbierung des Dreiecks mit der Folge, dass zwei rechtwinklige Dreiecke daraus entstehen (vgl.Abb.9). Segeben ist nun die Grundseite, die Höhe h und der Winkel von 36°. Bei einem rechtwinkligen Gegenkathete berechnet. Dreieck wird der Tangens über die Formel tan(a) Ankathete Hierbei ist die Höhe h die Gegenkathete und die Ankathete. Setze ich diese Werte ein, ergeben tan(36) =, nach Umstellung der Formel bekommt man für h = 1 Formel einsetze, ergibt sich für Apreieck = a •a* tan (36) die Formel - a * h zu vereinfachen. Wenn ich nun diesen Wert für h in die oben beschriebene gesamten Pentagons zu berechnen. AFünfeck = a* tan (36) Zum Schluss muss diese Formel mit dem Faktor 5 multipliziert werden, um den Flächeninhalt des 5+q² ¹a² tan (36) tan (36) 4.2.1. Der Goldene Schnitt a be Um den Flächeninhalt des Sterns zu erhalten, müssen von Afünfeck dann noch die fünf oben in Abbildung 7 beschriebenen Dreiecke subtrahiert werden. tan (36) 4.2. Geometrie eines Pentagramms Das Pentagramm besteht aus fünf gleichlangen Geraden. Es ist schwierig, ohne Hilfsmittel ein genaues Pentagramm zu zeichnen. Als ich selbst ein Pentagramm gezeichnet habe, bin ich dabei auf den goldenen Schnitt gestoßen. Daher habe ich ein Weg gesucht, den goldenen Schnitt für die Berechnung zu nutzen. Strecke Abb. 10: Goldener Schnitt ,,Eine bestimmte geometrische Teilung einer Strecke, bei der sich die größere Teilstrecke zur kleineren so verhält wie die Gesamtstrecke zum größeren Teil, wird seit etwa dem 19. Jahrhundert als ,,Goldener Schnitt" bezeichnet." (Springer-Verlag GmbH 2017) Diese Strecken werden vom Goldenen Schnitt also geteilt, wenn die Formel a (a+b) 8 a *5 => Das Hauptziel war es, a ag *5=> a = gilt. Die erste Entdeckung des Goldenen Schnittes stammt von Euklid (325 bis 270 vor Christus). Er wurde häufig in der Kunstepoche benutzt, um eine harmonische Aufteilung zu erzielen. (vgl. WDR1 2020) 1 Das Zeichen des Goldenen Schnitts ist Phi q. Der genaue Wert liegt bei q=+* √5 oder als ausgeschrieben Zahl p = 1.6180339887499. Wenn ein Goldener Schnitt vorliegt, wie hier bei der (a+b) Strecke I (I = a + b), gilt die Formel (vgl. Decker 2020, Springer Verlag 2017) Mit diesem o lässt sich Vieles an einem Pentagramm ausrechnen. Die oben erwähnte Formel = kann man einsetzen genauso wie die Gesamtstrecke I(I = a + b), b a (a + b) = b a a => 0 ===>1=a*y => a = a Eine weitere Formel ist I = a + b => b= I-a. 4.2.2. Umkreis und Innenkreis eines Pentagramms Für die Berechnung mithilfe des Goldenen Schnittes wird nur noch die Seitenlänge a benötigt. Die Formel für die Seitenlänge, die mit dem Radius des Umkreises berechnet wird, lautet a= * rc √10-2*√5. E rl 9 rc B C Abb. 11: Umkreis und Innenkreis Pentagramm 5. Berechnung des Flächenverhältnisses der US-amerikanischen Flagge 5.1. Einsetzen der Werte in die aufgestellten Formeln Das Seitenverhältnis der Flagge ist 10:19. Daher kann die Höhe beispielsweise als 1 angenommen werden und für die Breite 1,9. Da die Flagge unterschiedliche Größen annehmen kann, aber nur die Proportionen fixiert sind, rechne ich in Längeneinheiten. Aufgrund der Übersichtlichkeit verzichte ich auf die Nennung der Längeneinheiten. A = 1 L = -1/33 B= 1.9 D = 0,76 E = F = G = 130 7 130 1 156 A L D GHHHHHHHHHHG Abb. 12: US-amerikanische Flagge Der Durchmesser des Umkreises eines Sterns ist K= 0,0616. B Der Radius beträgt somit r = 0.0308. (vgl. Office of the federal Register 1963) 10 6. Lösung der Fragestellung Ich rechne mit den genauen Werten auf dem Taschenrechner. In dieser schriftlichen Rechnung runde ich jedoch das Ergebnis. Die Formel für die Seitenlänge lautet a= 뜰 *√10-2√5, nachdem der Radius eingesetzt 0.0308 2 √√10-2√5 -0.036208. wurde, ist a= Für den Flächeninhalt des Fünfecks wurde die Formel Apentagramm= 5*0.036208² tan (36) errechneten Wert für die Seitenlänge Apentagramm= ·*a* b²-². (Dorn et al. 2005) ADreieck = = * Da ich die zweite Methode gewählt habe, bei der die zusätzlichen Dreiecke von der Fläche des Pentagons abgezogen werden, müssen diese noch berechnet werden. Da die Formel, für den Flächeninhalt eines gleichschenkligen Dreiecks lautet, ADreiecka * a * h. Die Höhe h ist nicht gegeben, kann aber kann über die Seitenlänge b berechnet werden. Die Formel lautet h=√b² - ². Eingesetzt in die erste Formel ergibt sich: I= 0.036208 * ≈ 0.058585. =0.002256. Von dem Goldenen Schnitt ergibt sich die Formel I = a* p. Hierbei ist a=ag. Somit kann jetzt die Strecke I berechnet werden: Nun kann der Flächeninhalt der fünf Dreiecke berechnet werden. ADreiecke= 5 * * 0.036208 * 0.22378² 5.a² tan (36) Für das Dreieck benötig man b, wobei gilt b = 1−a = 0.058585 – 0.036208 ≈ 0.22378. 0.036208 2 11 hergeleitet, mit dem ≈ 0.001191 Zum Schluss muss die Fläche der Dreiecke von dem Flächeninhalt des Fünfecks subtrahiert werden. Apentagramm =Afünfeck-ADreieck=0.002256 -0.01191-0.001065 Da die Flagge 50 Sterne hat, muss auch die Fläche der 50 Sterne von der blauen Fläche subtrahiert werden. A50-50*0.001065~0.053246 Zu Beginn dieser Arbeit habe ich die Formeln für die Berechnung der Fläche der Farben aufgestellt. Nun kann ich jeden Wert ermitteln: Für Rot: Arotges=3* 1.9 +41 (1.9 -0,76) = 0.78923076923077 * Der Anteil der roten Fläche beträgt somit 41.538461538462%. Für weiß: Aweißges= 3. * 1.9 + 3 — * (1.9 – 0,76) + 0.053246 -0.75478419900127 13 13 Der Anteil der weißen Fläche beträgt somit 39.725484157962%. Für Blau: Ablauges * 0,76-0.053246 =0.035598503176796 Der Anteil der blauen Fläche beträgt somit 18.736054303577%. 7. Zusammenfassung der Ergebnisse In dieser Facharbeit habe mich mit dem Farbverhältnis der US-amerikanischen Flagge beschäf- tigt. Zunächst habe ich die Entstehung der US-amerikanische Flagge erläutert. Aufwändig war es, eine Formel zur Berechnung des Flächeninhalts der Sterne zu finden. Dabei bin ich auf das Pen- tagon gestoßen, für dessen Flächenberechnung ich eine Formel hergeleitet habe. Durch den gol- denen Schnitt konnte ich dann die fehlende Variabel berechnen und den Flächeninhalt der Sterne über den Umfang ausrechnen. Zum Schluss habe ich jeden Wert in die erarbeiteten Formeln ein- gesetzt und das Farbverhältnis mit einem Prozentanteil angegeben. 12 8. Quellenverzeichnis Decker, Susanne, Der Goldene Schnitt, 2020, Plantet Wissen: https://www.planet- wissen.de/natur/forschung/mathematik/pwiedergoldeneschnitt100.html#:~:text=Die%20erste%20gen aue%20Beschreibung%20des,325%20bis%20270%20vor%20Christus). Oman%20ihn%20in, 18:11 &text=Seitdem%20entdeckte%2 Goldene%20Schnitt%20in%20der%20Renaissance. aufgerufen am 26.04.2021 um Dorn, H., Freudigmann H., Herbst, M, et. Al, Formelsammlung Mathematik, Ernst Klett Verlag, 2005 Fisher, Lynn https://usflags.design/usa/#:~:text=The%20U.S.%20flag%20has%20a, the%20length%20of%20the%20fl y. aufgerufen am 27.04.2021 um 17:43 National Postal Museum, Long May It Wave, https://postalmuseum.si.edu/exhibition/long-may-it- wave-the-evolution-of-the-american-flag/the-legend-of-betsy-ross aufgerufen am 04.05.2021 um 18:21 Office of the federal Register, Code of Federal Regulations, Title 3 - The President, 1963., Seite 368 Springer-Verlag GmbH Deutschland, 2017 https://www.spektrum.de/lexikon/mathematik/der-goldene-schnitt/2514 aufgerufen am 26.04.2021 um 18:10 Shalev, Eran, The Creation, Design and Symbolism of the Stars and Stripes, in Vile, J. R., The American Flag - An Encyclopedia of the Stars and Stripes in U.S. History, Culture, and Law,ABC-Clio, 2018 WDR1, 2017, https://www1.wdr.de/stichtag/stichtag-sternenbanner-wird-flagge-der-usa-100.html Aufgerufen am 26.04.2021 um 19:00 13 9. Abbildungsverzeichnis Abbildung 1: US-amerikanische Flagge https://de.wikipedia.org/wiki/Flagge der Vereinigten Staaten#Siehe auch Abbildung 2: frühere Sons of Liberty Flagge https://de.wikipedia.org/wiki/Sons of Liberty Abbildung 3: Spätere Sons of Liberty Flagge https://de.wikipedia.org/wiki/Sons of Liberty Abbildung 4: Grand Union Flag https://commons.wikimedia.org/wiki/File:FAKE Grand Union Flag.png Abbildung 5: Flächen der US-amerikanischen Flagge https://www.ebay.de/itm/282770241533 Abbildung 6: Inneres Fünfeck https://www.mathespass.at/formeln/regelm%C3%A4%C3%9Figes-f%C3%BCnfeck-formeln-und- eigenschaften Abbildung 7: Die Dreiecke, die subtrahiert werden müssen, für den Flächeninhalt eines Pentagramms https://www.mathespass.at/formeln/regelm%C3%A4%C3%9Figes-f%C3%BCnfeck-formeln-und- eigenschaften Abbildung 8: Erster Ansatz https://commons.wikimedia.org/wiki/Das Pentagramm als manuelle SVG-Grafik (de) Abbildung 9: Zweiter Ansatz https://rechneronline.de/pi/fuenfeck.php Abbildung 10: Goldener Schnitt https://www.mathespass.at/formeln/regelm%C3%A4%C3%9Figes-f%C3%BCnfeck-formeln-und- eigenschaften Abbildung 11: Umkreis und Innenkreis Pentagramm https://rechneronline.de/pi/fuenfeck.php Abbildung 12: US-amerikanische Flagge https://de.wikipedia.org/wiki/Flagge der Vereinigten Staaten#Siehe auch 14 10.Anhang Office of the federal Register, Code of Federal Regulations, Title 3 - The President, 1963., Seite 368: -G-H--H- MAFILM STANDARD PROPORTIONS HOIST FLY HOIST FLY (WIDTH) LENGTH) (WIDTH) LENGTH) OF FLAG OF FLAG OF UNION OF UNION 1.9 76 8 1 5.385 ( C 0 #--- .054 E WHIC 054 063 063 F G 15 DIAMETER WIDTH OF OF STAR STRIPE .0616 0769 K L MU A DIVIDED INTO 13 EQUAL PARTS "L Shalev, Eran, The Creation, Design and Symbolism of the Stars and Stripes, in Vile, J. R., The American Flag - An Encyclopedia of the Stars and Stripes in U.S. History, Culture, and Law,ABC-Clio, 2018 The Flag in American Art Kenneth Hartvigsen In René Magritte's 1929 painting The Treachery of Images, viewers encounter a realistic-looking pipe above the slogan "Ceci n'est pas une pipe" (This is not a pipe). This may seem like a bit of surrealist fun, that the artist negated the image he created. The title, however, points toward more serious concerns. All images are treacherous because they are not what they appear to be. Magritte is right, this is not a pipe-it is a picture of a pipe. But is this always the case? In 1964, Alan R. Solomon asked a question about Jasper Johns's artwork Flag (1954)-which has 13 red and white stripes and a blue field of stars that would have made Magritte smile: "Is it a flag, or is it a painting?" he queried (Solomon 1964). This question is not as easy to answer as whether one could smoke some aged Cavendish using Magritte's painting. The easiest answer to Solomon's question would probably be yes. While Johns invited this confusion in various ways, the very nature of flags seems to confuse the relationship between a real thing and a representation. A flag is flexible, both literally and symbolically. When it flies, it shows the direction of the wind. Symbolically, it reveals prevalent attitudes and beliefs about the world in which it flies, and simultaneously that world reveals the flag's true shape. This essay analyzes six examples of flag art-two from the 19th century, three from the 20th, and one from the 21st-that behave almost like real flags by revealing prevalent "winds of change from their historical moment. These artworks are iconic; they are not, however, monolithic in meaning. Like real flags, they can mean different things to different people. By analyzing these artworks and their historical contexts, this essay will explain some of the ways that flags insert themselves into cultural discourse and how the art world has participated in creating the flag and the America that we know today. John Trumbull, Surrender of Lord Cornwallis In 2016, 22 million people visited Washington, D.C., and the United States National Park Service recorded 33.8 million individual visitors to the National Mall (Destination DC 2017). A highlight for many visitors was the United States Capitol, where John Trumbull's cycle of monumental history paintings is permanently installed in the rotanda. The Surrender of Lord Cornwallis (1820) is thus seen by millions of people every single year. In the center, Maj. Gen Benjamin Lincoln, astride a white charger, receives the sword of surrender from a British officer while lines of soldiers on both sides provide a visual balance that suggests tensions are now at rest. Subtle asymmetries in the background, however, hint at the turmoil that led to this. Smoke rises diagonally from behind the French forces on the viewer's left, and beneath the smoke, a seemingly endless column of British soldiers curves into view. Lincoln's horse bends to its left, its head pointing at Gen. George Washington, who presides from under the billowing folds and the authority of the Stars and Stripes. Washington and flag together manifest an iconographic center of gravity around which the rest of Turnbull's composition spins. The white flag flying on the painting's opposite side-a French flag flying above French soldiers-fies higher than the American flag, perhaps as a gesture on Trumbull's part that acknowledges the role Rochambeau's troops played in securing victory. Despite the flag's height, it arches downward, leading the eye toward Washington's rampant colors. The American flag, in contrast, billows upward, pointing out of the canvas toward a future dominated by an American story. Its fly, curling in the breeze, almost resembles a face in profile caught in a victorious shout. Though it may look unremarkable, this flag is an early design seen in other Trumbull paintings, with eight-pointed stars arranged in a square with one in the center. Based largely on its appearance in Trumbull's paintings, Grace Rogers Cooper supposed that this was an authentic early design (Cooper 1973, 9), but not all historians are convinced that Trumbull can be trusted when it comes to the details of his paintings (Guenter 1990, 35). Still, as a veteran of the war, Trumbull would have been familiar with the flags that were used. In his painting General George Washington at Trenton, the more familiar Betsy Ross design (five-pointed stars in a circle) flies over an artillery crew in the distance. Placed in the composition below General Washington's horse, this flag does not enjoy the same victorious position as its sibling at Yorktown but may be the earliest depiction of this more-familiar design in a painting (Cooper 1973, 9). Trumbull's use of multiple flag designs indicates that this young nation was still finding its way in the world. This is not to say that he intentionally used different flags for this reason, but if Cooper was correct that both of these designs were used during the war, Trumbull's awareness and use of these designs documents a time when America was still deciding what symbols it would use-a decision that would have wide-ranging effects. The son of the only colonial governor to support the and rose to the rank of colonel by the age of 21. A gifted artist from his youth who had e promising military career-after a disagreement with Congress about the date of a promotion and pursued art studies in England, of all places. Trambull was a first-hand witness to the flag's emergence as a symbol of international American masters, including the great Bostonian lion, Trumbull served for a time as George Washington's aide-de-camp portraitist John Singleton Copley while studying a at Harvard, Trumbull left his In England, Trumbull absorbed a European academic style infused with Benjamin West's and John Singleton Copley's flare for contemporary subjects. He also managed to get himself thrown in prison on suspicion of treason after he travelled to Paris to rendezvous with Benjamin Franklin and Thomas Jefferson. Though threatened with execution, he was released after seven months and returned to America. By 1783, he was back in London, where Benjamin West suggested the massive project for which Trumbull would forever be known-the history paintings commemorating the American Revolution that hang in the Capitol Rotunda (Stati 2011, 181). As West had taught him, Trumbull never let the literal truth get in the way of a good painting or a grand story. Nonetheless, Trumbull enjoyed a social position that allowed him to work with many of the individuals pictured in his paintings (Paulson 1982, 349). The resulting paintings became visual texts around which an evolving mythos of Revolutionary America could develop and were part of a program to rebuild the U.S. Capitol, which the British had burned in the War of 1812. As Stati explained, during and after the Revolution, the nation was "in urgent need of images, rituals, and mythologies not only that could replace the old British ones, but that might also bring a disparate population together in functional union (Staiti 2011, 7). While Staiti is writing of artwork, the flag itself was one of those tools used to construct these new mythologies. Its design represents the unification of the states, as its stars suggest the independent states rising together as a new constellation. It is no surprise that this need for images, a need for American icons, would merge with the arrival of the new American flag Emanuel Leutre, Washington Crossing the Delaware The European style that inspired Trumbull continued to be the dominant model for American history painters, as evidenced in the career of German American artist Emanuel Leutze. Born in Germany, raised in Virginia and Philadelphia, Leutze studied in Germany, where his best-known painting was influenced not only by European style but by political unrest. The Creation, Design, and Symbolism of the Stars and Stripes Eran Shalev A fateful resolution of the Naval Committee of the Continental Congress declared on June 14, 1777, that "the Flag of the thirteen United States, be Thirteen Stripes, alternate red and white; That the Union be Thirteen Stars, white in a Blue Field, representing a new Constellation." This laconic decree did not elaborate or explain the meaning of the flag's use of stripes or the colors red, white, and blue. It did not stipulate the shape or size of the stars, their order, or their layout. In fact, not until 1912, during the presidency of William Howard Taft, would the exact shape, arrangement, and proportions of the flag be established. The authorization of the flag and its design in 1777 were, according to one authority, "a highly practical affair, without fanfare"; hence we know nothing about the forces and motivations contained in the creation of the Stars and Stripes (New York Gazette and Weekly Mercury, April 28, 1783). Since the United States was the first modern nation, the adoption of a new national flag was by definition an unprecedented move. Unprecedented, it may have been, but as we have seen, its official order was also concise to the extreme. To understand the sparse language of the Flag Resolution, we must remind ourselves that early modern flags were not the effective vehicles for rallying national and patriotic passions that they are nowadays and that their symbolic meaning tended to be local and obscure. Flags served mostly as military standards for identification and communication devices, and it was at sea that their use as large, colorful, and distinguishable objects of identification had become established practice (hence Congress's naval committee's ordering of the Flag Resolution). In the colonies, Americans could glance at the English Union Jack waving over Crown property such as official buildings and military installations. They could but rarely would. As the North American colonies were overwhelmingly rural, most Americans spent their whole lives in the vicinity of their farms, and local centers of English power were few and far dispersed. Thus, a majority of colonial Americans rarely encountered flags, while many never even observed a billowing English flag. Consequently, in the English imperial world, flags did not spontaneously capture the average citizen's adoration. Even the American flag would become a universally revered and beloved icon of freedom and liberty only late in the 19th century, as a direct consequence of the Civil War. In paintings and drawings of the Early Republic, the flag often appears as a decorative element framing more-favored national icons, such as the goddess of liberty and George Washington. For a long while, the Stars and Stripes would stay on the margins of the cultural and symbolic world of the new nation. At the moment of imperial disintegration and the creation of the United States, the language of nationalism, including its visual lexicon, had yet to be born. That may explain the tardiness at which the new United States moved toward adopting a national flag, a concept that would mature only decades later. At a time when the use of a national flag was still limited to a small number of buildings, installations, and ships, a great seal seemed to be a more pressing issue (indeed, a special committee was asked to formulate such a device immediately following independence). It took almost a full year for the Second Continental Congress to pass the Flag Resolution, which was, at least in retrospect, minimalist to a fault. The congressional resolution on the flag left many variables, and their meanings, including the choice of colors, shapes, and proportions, were arcane. We may only attempt to come to terms with those fateful choices, deconstruct the motivations behind them, and reveal the ideas that drove them. It is a worthy endeavor, however, as those variables were important in creating the pervasive and revered visual language that still saturates our lives centuries later. 16 "That the flag of the thirteen United States be thirteen stripes" With the surge of colonial resistance to strong-handed imperial measures in the 1760s, local and symbolic representations began to show up on colonial standards and flags. Among those were the snake (likely Benjamin Franklin's creation), more specifically an indigenous rattlesnake, which symbolized vigilance and opposition; the liberty pole and the pine tree, which were local New England symbols of self-reliance and moral rectitude; and liberty caps and the Goddess of Liberty. These emerged as useful emblems for rallying support to the American cause, gaining traction in certain locales and times during the tumultuous revolutionary years. Among those local flags was the Rebellious Stripes, a banner first raised by the Sons of Liberty in 1767 and consisting of nine vertical red and white stripes in alternating order (Guenter 1990, 27). The Rebellious Stripes may have posed a precedent for the American Patriots, but it was not the direct predecessor of the American flag. That role was preserved for the Continental Colors, the first generally accepted continental flag, used between 1775 and 1777. Also known as the Great Union and the Grand Union Flag, the Continental Colors had 13 horizontal stripes of alternating red and white (as opposed to the Rebellious Stripes' vertical columns), meant to represent the unity of the 13 mainland colonies, with the crosses of St. George and St. Andrew adorning its canton (the upper inner quarter of the flag's field). The stripes manifested a degree of variation, as various flags displayed red and blue stripes, or red white and blue, and while 13 stripes was the norm, some had 9 (Teachout 2009, 30). Some of the choices for the design of the Continental Colors are somewhat perplexing. Was the retention of the British cross (which customarily represented the king of England or Scotland) an intentional gesture, hinting at the possibility of reconciliation, or was it a "signal of submission," as George Washington asserted (quoted in Guenter 1990, 28)? Whatever the reason may have been, that temporary flag never won the hearts and minds of the American rebels. Even as a banner for naval identification, for which it was predominantly used, it proved a poor choice, as its design made it difficult to distinguish from the British flag. It did bequeath, however, the concept of a single national flag, and its 13 horizontal alternating red and white stripes became established as a symbol of Confederate unity. "Alternate red and white... in a blue field" The anonymous designer(s) of the flag and the author of the decree that gave birth to it may have felt that the use of red, white, and blue as well as of a canton and field did not necessitate explanation because those elements were already in widespread use in late 18th-century flags and standards. Nevertheless, five years after the Flag Act was decreed, and in the context of elaborating on the design of the Great Seal, which bore similar colors, Congress bestowed meaning on that particular choice of colors: the white signified purity and innocence; the red signified vigor and valor; and the blue stood for vigilance, perseverance, and justice. However, as historian Arnaldo Testi points out, these may have been ex post facto rationalizations, as the colors may have well been adopted for prosaic, not affectionate, reasons. They were familiar from other designs, fabrics, and dyes that were in common use; in other words, the colors of the British flag were adopted because they were available for the struggling wartime and preindustrial economy of the young American nation (Testi 2010, 17). White purity, red valor, and blue vigilance were all surely noble, but it was their immediate accessibility that helped drive Americans to dye their flags with those recognizably English pigments. "Thirteen stars, white in a blue field... representing a new constellation" Accompanying the red and white horizontal stripes were 13 white stars, which appeared in a blue canton in the flag's upper-left corner. While each star obviously represented a state in the new confederacy, the vague and sparse specifications of the Flag Resolution meant that any possible arrangement of the stars would be theoretically legitimate. Consequently, there were numerous variations of the 13-star flag. A circular arrangement of stars was a favorite of painters, designers, and flag makers, since the ring suggested unity and perpetuity. Called the medallion pattern, that circular arrangement of fame is better known as the Betsy Ross flag, named after the Philadelphia seamstress whom myth credits with making the first American flag. That pattern was, however, only one of many variants that emerged during the evolutionary stage of the American flag, a time in which a spectacular variety of arrangements appeared and disappeared. The stars could be arranged in a full circle, sometimes in a circle of 12 with a central star (such as on the Cowpens Flag, further discussed below); in horizontal rows, sometimes forming a square frame around the blue center, in an arch over the number 76; and even forming the shape of a larger star. With the expansion of the republic, as additional stars were added to the original 13, they could appear in configurations in horizontal rows, in vertical columns, or in a square border. Star shapes varied too, as stars came with six or seven points, as in the heraldic tradition. Only occasionally did they have the now-familiar five points. Beyond the possible arrangement and exact shape and alignment of the stars, historians have struggled to determine their exact origin or even why a given star shape was used in the first place. While studies have been dedicated to the history of most of the elements contained in the American flag, the origins of the stars, the most distinct shapes imprinted on the flag, have remained more obscure and typically less explored (Fawcett 1937; Moeller 1976). Regardless of the prominent place of the symbol of the state as star and the consequent "American constellation" in the American political vocabulary (Keim and Keim 2007, 40- 42), vexillologists and historians of the American flag seem to have accepted somewhat unsubstantiated conjectures regarding the origins of this idiom. While many have simply disregarded the question of the stars' source or meaning, the leading assumptions of those who have explored the origins of the stars seem to be that they pedigree from the star-laden Masonic visual tradition or, alternatively, from the coat of arms of George Washington's family (Teachout 2009, 30). While remaining silent on all elements of the flag other than the stars, that the Resolution elaborated only the 13 states as forming "a new Constellation" points to the remarkable originality of the new American flag: the flag implied that United States was written in the skies, a novel and unprecedented political constellation. It is thus worth dwelling upon the symbol of the state as star and the consequent image of the United States as a new constellation, as it involved a remarkable intellectual reconfiguration tightly linked to the emergence of American republicanism and nationhood. Bearing in mind how little we know beyond the actual wording of the Flag Resolution, it may be futile to investigate the exact moment of origin, or identity of the originator, of the representation of the star as state. It would be more fruitful to uncover the meaning and significance of that epoch-making language. The republicanism and anti-monarchism of the American Revolution shattered a traditional conception of political order based on the imagery of a single solar power center. In the European world of monarchic absolutism, kings were viewed as suns, an outlook epitomized in the image of Louis XIV but prevalent across the continent, England included. In that view, kings were suns placed in the middle of a solar "system," the nation, which reigned over harmoniously revolving "planets" (traditionally understood as standing for either social orders, state apparatuses, or magistrates). A crucial revolutionary move took place in America: from a monarchic sun, the political universe was transformed into an egalitarian starry constellation from a celestial kingly hierarchy to an astro- republican (nonmonarchical) firmament. The revolution (initially, we should remind ourselves, an astronomic term denoting the rotation of the heavens) gave rise to a wholly new mode of communicating the political-national order. Now, with the American states viewed as stars, no single sun or kingly star overshadowed and dominated others; together the American state-stars constituted a novel political system in which a plurality of individual stars held together. comprising a republican "constellation" that was more perfect than its discrete parts. Instead of a realm in which all politics revolved around the sunlike king, in the 1770s an alternative and revolutionary political cosmology emerged and was enshrined in the new nation's symbols: a diffuse constellation of uniform floating stars devoid of a solar center, a constellation that embodied egalitarian and republican values. Throughout the republic's founding and expansion and the consequent addition of stars to the "new American constellation," and even when it temporarily collapsed during the Civil War, that constellational image has provided a distinct vocabulary to articulate and express Americans' shifting attitudes toward, and understanding of, their unique nation. This idea that a republican solar system was benevolent and benign, not monarchically coercive, was expressed graphically during the years following its adoption, first and foremost on the flag but also on the likes of paper money and other insignia. As we have already seen, that image had several variations in its initial evolution. Within the process of the formation of the Star-Spangled Banner, the Cowpens Flag signifies a link in the evolution from a solar to a constellational model of the American flag. that celebrated flag, which was famously carried during its namesake battle (1781) by the 3rd Maryland Regiment, 12 states were represented by stars revolving around a 13th similar, central star. Tellingly, the central star (presumably standing for Maryland, but potentially representing any of the states) was a five-point-star design indistinguishable from the rest of the stars in the constellation. In the Cowpens design, the central body was still distinguishable through its pivotal position, but it was not a domineering sun anymore. The American flag would abandon a hierarchal 17 representation and eventually convey the fully egalitarian constellational model, boasting indistinguishable state-stars, of the American republican federacy. While the ideas behind the Flag Resolution, adopted with little ceremony by the obscure marine committee of the Congress, do not echo with modern audiences, politically conscious Americans seem to have understood perfectly well the motivations behind the design of the new flag and its novel starry symbolism in particular. In a letter that paraphrased the wording of the Resolution, Benjamin Franklin, who had not surprisingly for such a Renaissance man lifelong interest in astronomy, was proud to acquaint the ambassador of Naples with "the Flag of the United States of America [that] consists of thirteen Stripes, alternately red, white and blue; a small Square in the upper angle, next the flag staff, is a blue field, with thirteen white Stars, denoting a new Constellation" (Sparks 1829, 1:470.). Notably, Franklin took the Flag Resolution's example in elaborating only on the novel celestial element of the flag. Benjamin Rush, another revolutionary scientific and political savant, proposed on October 21, 1777, to introduce "a constellation to be worn on the breast containing 13 stars as a reward for military exploits" (Taylor 2006, 5:319). And on April 16, 1778, the Bostonian Patriot James Lovell revealingly remarked in a letter to Abigail Adams that "the rising Constellation which is now in place of the British Union [Jack] is a Device greatly admired in our Colours" (Smith 1976. 9:423). Ezra Stiles, president of Yale University, commented that "The Congress have substituted a new Constella of Stars (instead of the Union) in the Continental Colours" (quoted in Furlong and McCandless 1981, 101-2). The United States was viewed from the outset as a new constellation that replaced a corrupt older European solar-monarchical system. A republican assemblage of stars formed that constellation, an idea still manifested on numerous flag poles across the land, even if its original meaning has been since lost and obscured. Influence On April 4, 1818, President James Monroe signed an act that "Provided for 13 stripes and one star for each state, to be added to the flag on the 4th of July following the admission of each new state." This official decree stipulated what contemporaries hoped: additional stars would not ruin the federal harmony and balance but rather strengthen the American republican constellation. By then, Americans of the early republic had formulated and perpetuated a powerful political cosmology that analogized celestial bodies to the American political world. State flags indicate the pervasiveness of that language: 17 out of the 37 (46 percent of) American states that joined the Union after 1776 explicitly included stars on their flags. Most notable, perhaps, was Texas, "the Lone Star Republic," which was founded as an independent state under the sphere of American political culture and eventually attached its star-spangled state-banner to the incrementally growing constellation. The "new American constellation," the image of the American federation as a fraternity of stars, which originated deus ex machina in the Flag Resolution of 1777, is consequently manifested on countless flagpoles, currency notes, and numerous other cultural mannerisms. No less striking is the fact that the United States provided starry inspiration not only to the states that joined the Union but also to numerous nations and states that established their independence during the 19th century and beyond. Scores of new countries, from the Philippines and Australia to Brazil, took their cue from the American starry idiom and adorned their national flags with shining stars. A remarkable array of polities as diverse as the European Union and the Cook Islands incorporated rings of stars into their flag designs. If many nations are chosen, as the revealing title of a study of national chosenness indicates (Smith 2004), many likewise seem to perceive themselves as written in the skies. In this light, the connection between the Stars and Stripes and those complex ideas associated with exceptionalism seems somewhat ironic: While Americans came to understand themselves in celestial-exceptional terms, they also paved the way for other nations to understand themselves in similar terms. The United States' heavenly image has thus not only shaped Americans' understanding of their nation but has also had a powerful global effect on the ways in which numerous communities around the world imagine themselves. The state as star and consequent image of the American constellation, born uneventfully in a mundane wartime pronouncement of the Continental Congress, has become remarkable evidence of America's wielding of soft power. The American flag was the first modern national flag. Unlike its predecessors, it did not represent a sovereign or a monarchic dynasty, nor was it centered on a coat of arms. Moreover, it was used liberally and was not confined to military installations and ships. It was a new breed, a cloth that represented a people, a nation state. The Stars and Stripes was the creation of a republican revolution: egalitarian, without a symbolic monarchical center to which to pay homage. It would take years (and a civil war) before the flag could truly become a democratic symbol of popular identity that would enter, literally, into people's homes and 11.Erklärung der selbstständigen Arbeit Erklärung Hiermit erkläre ich, dass ich die vorliegende selbstständig und ohne fremde Hilfe verfasst und keine als die im Quellenverzeichnis angegebenen Hilfsmittel verwendet habe. Insbesondere versichere ich, dass ich alle wörtlichen und sinngemäßen Übernahmen aus anderen Werken als solche kenntlich gemacht habe. Münster den 04.05.2021 18