Spirograph,Spirograph inventors | edubilla.com : Denys Fisher About Invention Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965. Bruno Abakanowicz is widely credited as inventor of Spirograph which is kind of very important instrument in mathematics. It can be considered as toy that is used in geometry in mathematics but its functions are very important. It is used for producing roulette curves in mathematical format. These curves are termed as epitrochoids and hypotrochoids. It is also used in many software and that to describe those, which work on the same principal of these mathematical curves. It is also termed as a synonym of epitrochoid because of its work which is much similar to this unique instrument. Bruno invented the Spirograph in any time between the decades of 1880s and 1890s but the actual time is not known. The spirograph design by him was used for variety of tasks at that time.

If there was any area which was delimited by curves then the spirograph was used to use to measure that area at that time. Spirograph - YouTube Spirograph Want to watch this again later? Sign in to add this video to a playlist. Need to report the video? Sign in to report inappropriate content. The interactive transcript could not be loaded. Loading... Rating is available when the video has been rented. This feature is not available right now. Please try again later. Published on Dec 11, 2014 Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965. The name has been a registered trademark of Hasbro, Inc., since it bought the Denys Fisher company. The Spirograph brand was relaunched with original product configurations in 2013 by Kahootz Toys. This video is targeted to blind users.

Attribution: Article text available under CC-BY-SA Creative Commons image source in video Category Spirograph - Wikipedia, the free encyclopedia Spirograph Jump to: navigation , search This article includes a list of references or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations where appropriate . (April 2009) Several Spirograph designs drawn with a Spirograph set. Spirograph is a geometric drawing toy that produces mathematical curves of the variety technically known as hypotrochoids and epitrochoids . The term has also been used to describe a variety of software applications that display similar curves, and applied to the class of curves that can be produced with the drawing equipment (so in this sense it may be regarded as a synonym of hypotrochoid). The name is a registered trademark of Hasbro , Inc. Contents [ edit ] History The Spirograph was invented by British engineer Denys Fisher who exhibited it in 1965 at the Nuremberg International Toy Fair . It was subsequently produced by his company. Distribution rights were acquired by Kenner , Inc., which introduced it to the United States' market in 1966.

[ edit ] Operation Example of a Spirograph set produced and sold in the USSR in the 1980s. A Spirograph consists of a set of plastic gears and other shapes such as rings, triangles, or straight bars. There are several sizes of gears and shapes, and all edges have teeth to engage any other piece. For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings. To use it, a sheet of paper is placed on a heavy cardboard backing, and one of the plastic pieces is pinned to the paper and cardboard. Another plastic piece is placed so that its teeth engage with those of the pinned piece. For example, a ring may be pinned to the paper and a small gear placed inside the ring – the actual number of arrangements possible by combining different gears is very large. The point of a pen is placed in one of the holes in the moving piece. As the moving part is moved the pen traces out a curve. The pen is used both to draw and provide locomotive force; some practice is required before Spirograph can be operated without disengaging the fixed and moving pieces.

More intricate and unusual-shaped patterns may be made through the use of both hands, one to draw and one to guide the pieces. It is possible to move several pieces in relation to each other (say, the triangle around the ring, with a circle "climbing" from the ring onto the triangle), but this requires concentration or even additional assistance from other artists. About: Spirograph About: Spirograph An Entity of Type : Thing , from Named Graph : , within Data Space : dbpedia.org Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.It was developed by British engineer Denys Fisher and first sold in 1965.The name has been a registered trademark of Hasbro Inc. since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched with original product configurations in the USA in 2013 by Kahootz Toys and in Europe by Goldfish and Bison.

Property abstract Le Spirographe, marque déposée par Hasbro, est un instrument de dessin permettant de tracer des figures géométriques, des courbes mathématiques techniquement connues sous le nom d'hypotrochoïdes. Le mot est également utilisé dans des logiciels qui montrent des courbes semblables. Le Spirographe a été inventé par Denys Fisher, qui l'a présenté en 1965 au Salon du jouet de Nuremberg. Les droits de distribution ont été acquis par Kenner, qui l'introduit sur le marché américain en 1966. Le Spirographe est composé de différentes roues et d'anneaux dentés en plastique transparent. Les roues sont les pièces mobiles, et se positionnent dans les anneaux, pièces fixes, de manière à pouvoir y tourner grâce au système d'engrenages. Une feuille de papier est fixée sur le plateau à l'aide de goupilles en plastique.

Le plateau est lui-même composé d'une bordure dentée, sur laquelle on peut fixer une règle ou directement les anneaux dentés. Il suffit ensuite de placer une roue dentée dans l'anneau, et une pointe de stylo à bille dans l'un de ses trous pour pouvoir tracer une courbe sur le papier. Le stylo est utilisé à la fois pour dessiner et pour fournir la force motrice. Une certaine pratique est nécessaire avant que le Spirographe ne puisse être actionné sans désengrener les pièces fixes et mobiles. Une version simplifiée avec 5 anneaux/roues prisonniers a été éditée par Miro-Meccano sous le nom de Cyclograph. (fr) Spirograph ist ein geometrisches Spielzeug, mit dem man verschiedene Muster oder mathematische Kurven zeichnen kann. (de) Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.It was developed by British engineer Denys Fisher and first sold in 1965. The name has been a registered trademark of Hasbro Inc.

since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched with original product configurations in the USA in 2013 by Kahootz Toys and in Europe by Goldfish and Bison. (en) Lo Spirograph è uno strumento che produce un tipo di curve chiamate ipotrocoidi e epicicloidi. Lo Spirograph è stato inventato dall'ingegnere britannico Denys Fisher, che lo presentò nel 1965 alla Nuremberg International Toy Fair. Lo strumento fu prodotto dall'azienda di Fisher, ma l'anno seguente i diritti di distribuzione vennero acquistati dalla Kenner, un'azienda di giocattoli statunitense, che iniziò a venderlo negli USA. In Italia è stato commercializzato con il nome di spirografo o cerchio magico. (it) El Espirógrafo es un juguete para diseño geométrico. El espirógrafo produce curvas matemáticas conocidas como hipotrocoides y epitrocoides.

El término también ha sido usado para describir varias aplicaciones de software que muestran curvas similares. es un producto registrado por Hasbro, Inc. (es) スピログラフ（英: Spirograph）は、曲線による幾何学模様を描くための定規の一種である。主に玩具店で販売されていることから玩具ともみなされている。 商標「SPIROGRAPH」はハズブロが登録している（日本では登録番号第2307176号、称呼(参考)「スピログラフ」、権利者氏名又は名称「ハズブローインコーポレイテッド」）。 (ja) Spirograf – przyrząd do kreślenia spiral oraz skomplikowanych krzywych matematycznych jak hipotrochoida czy epicykloida. Wynaleziony i opatentowany w XIX wieku przez polskiego matematyka Brunona Abakanowicza.

Ponownie opatentowany w 1965 roku przez angielskiego inżyniera Denys Fishera, który zaprezentował go jako zabawkę dla dzieci na wystawie Nuremberg International Toy Fair w 1965 roku. Obecnie spirograf jest zarejestrowany przez przedsiębiorstwo Hasbro, Inc. jako zabawka geometryczna. Prawa dystrybucyjne posiada przedsiębiorstwo Kenner, Inc., która wprowadziła ją na rynek amerykański w 1966 roku. (pl) Een spirograaf is een instrument dat gebruikt wordt om geometrische patronen te tekenen. De spirograaf werd bedacht door Denys Fisher (1918 - 2002), een Engels ingenieur.

Het principe bestaat uit een set ronde schijven van kunststof met tandwielen en een aantal andere voorwerpen, zoals ringen, driehoeken, rechte strips, ook voorzien van tandwielen, waarbij de ronde schijven door middel van de tandwielen over, of (in geval van de ringen) binnen de andere voorwerpen kunnen rollen. In de rollende schijven bevinden zich diverse gaatjes waardoor een potlood of pen met dunne punt kan worden gestoken. Door de stralen van de schijven en de positie van het gaatje te variëren kunnen tal van patronen worden vervaardigd. Een geavanceerde versie van de spirograaf werd toegepast bij het ontwerpen van patronen voor bankbiljetten en andere waardepapieren. Tegenwoordig kan men dergelijke patronen ook met een eenvoudige Java-applicatie tekenen. (nl) Espirógrafo é um produto registrado da Hasbro, Inc., um brinquedo para desenho geométrico.

O espirógrafo produz curvas matemáticas conhecidas como hipotroclóides e epitroclóides. O termo tem sido usado para descrever várias aplicações de softwares que mostram curvas similares. (pt) Спирограф — детская игрушка, состоит из пластмассовой пластины с вырезанными кругами разных диаметров и набора колёс меньшего диаметра с отверстиями внутри. Края кругов и колёс зубчатые, чтобы предотвратить проскальзывание. Метод использования: пластина прикладывается к листу бумаги, внутрь выбранного кругового отверстия помещается одно из зубчатых колёс, в одно из отверстий которого вставляется шариковая ручка или карандаш.

Затем зубчатое колесо приводится в движение лёгким нажимом на пишущий элемент, который оставляет на бумаге спиральный след.Вместо внутреннего зубчатого колеса (круга) могут быть использованы фигуры другой формы: треугольники, овалы и т. д. Кроме того, может быть использовано несколько фигур одновременно (треугольник вращается вокруг круга, катящегося по внутренней стороне шестиугольника, или круг вращается внутри другого круга, катящегося внутри третьего круга, но в другую сторону и с другой скоростью). Это позволит получить кривые новой формы. Многие из таких кривых невозможно построить в одиночку, без помощи другого человека.

(ru) 萬花尺 (日文：スピログラフ，俗稱デザイン定規，英文：Spirograph，俗稱Design Ruler) 是一種繪圖玩具，由外圖板及內圓圖板兩部分組成。內圓圖板像一個齒輪，沿圓心不同半徑的位置帶有許多筆洞，外圖板為一類似為內齒輪的大型圓孔，內圓板放在外圖板的圓洞中，循著圓周轉動，以鉛筆或原子筆從筆洞可以畫出像花朵一樣規則圖案。有些萬花尺會配有幾個不同半徑的內圓圖板。萬花尺所畫出的圖案，與外圖板圓圈半徑、內圓圖板半徑及筆洞位置有相關性。圖案令人聯想到萬花筒，故名萬花尺。從數學(尤其是解析幾何)觀點觀察，內圓板放在外圖板的圓洞中，循著圓周轉動所畫出的圖案是內旋輪線；兩個內圓板互貼，固定其中一個內圓板，讓另一

個可活動內圓板沿著固定內圓板轉動所畫出的圖案是外旋輪線；外圖板為長方形之內挖出大圓孔，如果外圖板的長方形外框上具有齒輪(一般沒有，只有刻度供兒童當直尺使用)的話，內圓板沿著長方形外框轉動所畫出的圖案是短擺線 (zh) Spirograph ist ein geometrisches Spielzeug, mit dem man verschiedene Muster oder mathematische Kurven zeichnen kann.

(de) Lo Spirograph è uno strumento che produce un tipo di curve chiamate ipotrocoidi e epicicloidi. Lo Spirograph è stato inventato dall'ingegnere britannico Denys Fisher, che lo presentò nel 1965 alla Nuremberg International Toy Fair. Lo strumento fu prodotto dall'azienda di Fisher, ma l'anno seguente i diritti di distribuzione vennero acquistati dalla Kenner, un'azienda di giocattoli statunitense, che iniziò a venderlo negli USA. In Italia è stato commercializzato con il nome di spirografo o cerchio magico. (it) El Espirógrafo es un juguete para diseño geométrico. El espirógrafo produce curvas matemáticas conocidas como hipotrocoides y epitrocoides. El término también ha sido usado para describir varias aplicaciones de software que muestran curvas similares. es un producto registrado por Hasbro, Inc.

(es) Spirograf – przyrząd do kreślenia spiral oraz skomplikowanych krzywych matematycznych jak hipotrochoida czy epicykloida. Wynaleziony i opatentowany w XIX wieku przez polskiego matematyka Brunona Abakanowicza. Ponownie opatentowany w 1965 roku przez angielskiego inżyniera Denys Fishera, który zaprezentował go jako zabawkę dla dzieci na wystawie Nuremberg International Toy Fair w 1965 roku. Obecnie spirograf jest zarejestrowany przez przedsiębiorstwo Hasbro, Inc. jako zabawka geometryczna. Prawa dystrybucyjne posiada przedsiębiorstwo Kenner, Inc., która wprowadziła ją na rynek amerykański w 1966 roku. (pl) Espirógrafo é um produto registrado da Hasbro, Inc., um brinquedo para desenho geométrico.

O espirógrafo produz curvas matemáticas conhecidas como hipotroclóides e epitroclóides. O termo tem sido usado para descrever várias aplicações de softwares que mostram curvas similares.

(pt) 萬花尺 (日文：スピログラフ，俗稱デザイン定規，英文：Spirograph，俗稱Design Ruler) 是一種繪圖玩具，由外圖板及內圓圖板兩部分組成。內圓圖板像一個齒輪，沿圓心不同半徑的位置帶有許多筆洞，外圖板為一類似為內齒輪的大型圓孔，內圓板放在外圖板的圓洞中，循著圓周轉動，以鉛筆或原子筆從筆洞可以畫出像花朵一樣規則圖案。有些萬花尺會配有幾個不同半徑的內圓圖板。萬花尺所畫出的圖案，與外圖板圓圈半徑、內圓圖板半徑及筆洞位置有相關性。圖案令人聯想到萬花筒，故名萬花尺。從數學(尤其是解析幾何)觀點觀察，內圓板放在外圖板的圓洞中，循著圓周轉動所畫出的圖案是內旋輪線；兩個內圓板互貼，固定其中一個內圓板，讓另一個

可活動內圓板沿著固定內圓板轉動所畫出的圖案是外旋輪線；外圖板為長方形之內挖出大圓孔，如果外圖板的長方形外框上具有齒輪(一般沒有，只有刻度供兒童當直尺使用)的話，內圓板沿著長方形外框轉動所畫出的圖案是短擺線 (zh) Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.It was developed by British engineer Denys Fisher and first sold in 1965.The name has been a registered trademark of Hasbro Inc.

since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched with original product configurations in the USA in 2013 by Kahootz Toys and in Europe by Goldfish and Bison. (en) Le Spirographe, marque déposée par Hasbro, est un instrument de dessin permettant de tracer des figures géométriques, des courbes mathématiques techniquement connues sous le nom d'hypotrochoïdes. Le mot est également utilisé dans des logiciels qui montrent des courbes semblables.Le Spirographe a été inventé par Denys Fisher, qui l'a présenté en 1965 au Salon du jouet de Nuremberg. Les droits de distribution ont été acquis par Kenner, qui l'introduit sur le marché américain en 1966.Une version simplifiée avec 5 anneaux/roues prisonniers a été éditée par Miro-Meccano sous le nom de Cyclograph.

(fr) スピログラフ（英: Spirograph）は、曲線による幾何学模様を描くための定規の一種である。主に玩具店で販売されていることから玩具ともみなされている。商標「SPIROGRAPH」はハズブロが登録している（日本では登録番号第2307176号、称呼(参考)「スピログラフ」、権利者氏名又は名称「ハズブロー インコーポレイテッド」）。 (ja) Een spirograaf is een instrument dat gebruikt wordt om geometrische patronen te tekenen.

De spirograaf werd bedacht door Denys Fisher (1918 - 2002), een Engels ingenieur.Het principe bestaat uit een set ronde schijven van kunststof met tandwielen en een aantal andere voorwerpen, zoals ringen, driehoeken, rechte strips, ook voorzien van tandwielen, waarbij de ronde schijven door middel van de tandwielen over, of (in geval van de ringen) binnen de andere voorwerpen kunnen rollen. In de rollende schijven bevinden zich diverse gaatjes waardoor een potlood of pen met dunne punt kan worden gestoken. Door de stralen van de schijven en de positie van het gaatje te variëren kunnen tal van patronen worden vervaardigd. (nl) Спирограф — детская игрушка, состоит из пластмассовой пластины с вырезанными кругами разных диаметров и набора колёс меньшего диаметра с отверстиями внутри.

Края кругов и колёс зубчатые, чтобы предотвратить проскальзывание. Метод использования: пластина прикладывается к листу бумаги, внутрь выбранного кругового отверстия помещается одно из зубчатых колёс, в одно из отверстий которого вставляется шариковая ручка или карандаш. (ru) 74 Spirograph Brushes by PS-Brushes | GraphicRiver Add to Collection 74 Spirograph Brushes “Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965.” – Wikipedia Content: Spirograph - 必应 Sign in Spirograph Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965. The name has been a registered trademark of Hasbro Inc.

since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched with original product configurations in the USA in 2013 by Kahootz Toys and in Europe by Goldfish and Bison. 7 2312 Spirograph Turtle Python Does anybody here knows how to play with turtle and has an idea how to use turtle?I have trouble getting the thing to work as the picture shown below.

[Ignored the colors]Image: turtle import * from math import * def formulaX(R, r, p, t): x = (R-r)*cos(t) - (r+p)*cos((R-r)/r*t) def formulaY(R, r, p, t): y = (R-r)*sin(t) - (r+p)*sin((R-r)/r*t) def t_iterating(R, r, p): t = 2*pi up() goto(formulaX, formulaY) down() while (True): t = t+0.01 formulaX(R, r, p, t) formulaY(R, r, p, t) def main(): R = int(input("The radius of the fixed circle: ")) r = int(input("The radius of the moving circle: ")) p = int(input("The offset of the pen point, between <10 - 100>: ")) if p < 10 or p > 100: input("Incorrect value for p!") t_iterating(R, r, p) input("Hit enter to close...") main()' I am trying to make that kind of shape. Here is the coding I have done so far.

I am bad at python.Thank you. I need help. Thanks! 图片: 图片: 答 Try changing your t_iterating function to this:def t_iterating(R, r, p): t = 2*pi # It seems odd to me to start from 2*pi rather than 0. down() while t < 20*pi: # This loops while t go...

python 3.4 spirograph error from turtle import* from math import* def Xcord(R,r,p,t): x= (R-r) * cos(t) - (r+p) * cos((R-r)//r*t) def Ycord (R,r,p,t): y= (R-r) * sin(t) - (r+p) * sin((R-r)//r*t) def t_iter(R,r,p): t=0 down() goto(Xcord(R,r,p,t),Ycord(R,r,p,t)) while (t < 2 * pi): t = t+.01 Xcord(R,r,p,t) Ycord(R,r,p,t) up() return def main(): R=100 r=4 p=int(input("Please enter a number between 10 and 100: ")) if p < 10 or p > 100: input(" Incorrect value of p!") t_iter(R,r,p) input("Hit enter to close porgram") bye() main() I get this error:Traceback (most recent call last): File "C:/Users/Coscio/Desktop/spirals.py", line 31, in <module> main() File "C:/Users/Cosc

io/Desktop/spirals.py", line 27, in main t_iter(R,r,p) File "C:/Users/Coscio/Desktop/spirals.py", line 13, in t_iter goto(Xcord(R,r,p,t),Ycord(R,r,p,t)) File "<string>", line 1, in goto File "D:\Python\lib\turtle.py", line 1774, in goto self._goto(Vec2D(*x)) TypeError: type object argument after * must be a sequence, not NoneType 图片: 图片: 答 从龟进口来自数学import定义Xcord ( R r p、t )：返回( r-r ) cos ( t ) - ( r + p ) cos ( ( r-r ) / / r t )高清Ycord ( R r p、t )：返回( r-r )罪( t ) - ( r + p ) sin ( ( r-r ) / / r t )高清t_iter ( R r。 。 。 from turtle import* from math import* def Xcord(R,r,p,t): x= (R-r) * cos(t) - (r+p) * cos((R-r)//r*t) def Ycord (R,r

,p,t): y= (R-r) * sin(t) - (r+p) * sin((R-r)//r*t) def t_iter(R,r,p): t=0 down() goto(Xcord(R,r,p,t),Ycord(R,r,p,t)) while (t < 2 * pi): t = t+.01 Xcord(R,r,p,t) Ycord(R,r,p,t) up() return def main(): R=100 r=4 p=int(input("Please enter a number between 10 and 100: ")) if p < 10 or p > 100: input(" Incorrect value of p!") t_iter(R,r,p) input("Hit enter to close porgram") bye() main() I get this error:Traceback (most recent call last): File "C:/Users/Coscio/Desktop/spirals.py", line 31, in <module> main() File "C:/Users/Coscio/Desktop/spirals.py", line 27, in main t_iter(R,r,p) File "C:/Users/Coscio/Desktop/spirals.py", line 13, in t_iter goto(Xcord(R,r,p,t),Ycord(R,r,p

,t)) File "<string>", line 1, in goto File "D:\Python\lib\turtle.py", line 1774, in goto self._goto(Vec2D(*x)) TypeError: type object argument after * must be a sequence, not NoneType 图片: 图片: 答 from turtle import* from math import* def Xcord(R,r,p,t): return (R-r) * cos(t) - (r+p) * cos((R-r)//r*t) def Ycord (R,r,p,t): return (R-r) * sin(t) - (r+p) * sin((R-r)//r*t) def t_iter(R,r,...

Rephrase spirograph code into function I'm writing a python spirograph program, and I need some help with converting part of it into a function. The code is attempting to reproduce the result illustrated in the video I found here. One line rotates around the origin, and then another rotates off the end of that, etc.With a little bit of research into (what I think is) trigonometry, I put together a function rotate(point, angle, center=(0, 0)). The user inputs a point to be rotated, the angle (clockwise) that it is to be rotated by, and the centerpoint for it to be rotated around.Then, I implemented an initial test, whereby one line rotates around the other. The end of the second line draws as if it were holding a pen.

The code's a little messy, but it looks like this.x, y = 0, 0 lines = [] while 1: point1 = rotate((0,50), x) point2 = map(sum,zip(rotate((0, 50), y), point1)) if x == 0: oldpoint2 = point2 else: canvas.create_line(oldpoint2[0], oldpoint2[1], point2[0], point2[1]) lines.append( canvas.create_line(0, 0, point1[0], point1[1]) ) lines.append( canvas.create_line(point1[0], point1[1], point2[0], point2[1]) ) oldpoint2 = point2 tk.update() x += 5 if x > 360 and y > 360: x -= 360 canvas.delete("all") time.sleep(1) y += 8.8 if y > 360: y -= 360 for line in lines: canvas.delete(line) lines = [] Great, works perfectly. My ultimate goal is what's in the video, however.

In the video, the user can input any arbitrary number of arms, then define the length and angular velocity for each arm. Mine only works with two arms. My question, ultimately, is how to put the code I posted into a function that looks like drawSpiral(arms, lenlist, velocitylist). It would take the number of arms, a list of the velocities for each arm, and a list of the length of each arm as arguments. What I've TriedI've already attempted this several times. Initially, I had something that didn't work at all. I got some cool shapes, but definitely not the desired output.

I've worked for a few hours, and the closest I could get was this:def drawSpiral(arms, lenlist, velocitylist): if not arms == len(lenlist) == len(velocitylist): raise ValueError("The lists don't match the provided number of arms") iteration = 0 while 1: tk.update() iteration += 1 #Empty the list of points pointlist = [] pointlist.append((0, 0)) #Create a list of the final rotation degrees for each point rotations = [] for vel in velocitylist: rotations.append(vel*iteration) for n in range(arms): point = tuple(map(sum,zip(rotate((0, lenlist[n]), rotations[n], pointlist[n])))) pointlist.append(point) for point in pointlist: create_point(point) for n in range(arms): print pointlist[n], pointlist[n+1] This is fairly close to my solution, I feel, but not quite there. Calling drawSpiral(2, [50, 75], [1, 5]) looks like it might be producing some of the right points, but not connecting the right sets.

Staring at it for about an hour and trying a few things, I haven't made any progress. I've also gotten pretty confused looking at my own code. I'm stuck! The point rotating around the center is attached to a point that is just flying diagonally across the screen and back. The line attached to the center is stretching back and forth. Can someone point me in the right direction?Results of further testsI've set up both functions to plot points at the ends of each arm, and found some interesting results. The first arm, in both cases, is rotating at a speed of 5, and the second at a speed of -3. The loop, outside of the function, is producing the pattern: The function, called with drawSpiral(2, [50, 50], [5, -3]), produces the result of It seems to be stretching the top half. With both arms having a velocity of 5, the function would be expected to produce two circles, one larger than the other. However, it produces an upside-down cardioid shape, with the point connected to the center. Now there's more evidence, can anyone who understands math more than me help me?

图片: 图片: 图片: 图片: 图片: 答 Your error is in for n in range(arms): point = tuple(map(sum,zip(rotate((0, lenlist[n]), rotations[n], pointlist[n])))) pointlist.append(point) Specifically,rotate((0, lenl... C# spirograph on a panel… how to save as BMP? I am using Graphics on a Panel to generate a spirograph, but when I try to save the drawing as a BMP (or whatever file extension), the file only takes the background of the panel, but the spirograph is not there!

Anyone knows a way around?int rayonA = Convert.ToInt32(txtCercleFixe.Text); int rayonB = Convert.ToInt32(txtCercleNonFixe.Text); int distance = Convert.ToInt32(txtPenDistance.Text); int pointsParCourbe = Convert.ToInt32(txtPointsParCourbe.Text); int TypeCourbe = 0; Graphics dessin = pnlSpiro.CreateGraphics(); public void DessinHypotrochoid(ref Graphics dessin, PointF ptOrigin, int rayonA, int rayonB, int distance, int pointParCourbe, int PFC, int rouge, int vert, int bleu,bool random) { // Dim angleStep As Double = radiansPerCircle / PointsPerCurve double angleStep = radians / pointParCourbe; //' Compute number of revolutions.

//Dim NumRevolutions As Integer = (bRadius / HighestCommonFactor(Math.Round(aRadius), Math.Round(bRadius))) int NumRevolution = rayonB / PFC; //' Total number of points to generate //Nombre de points totaux à générer //Dim NumPoints As Integer = PointsPerCurve * NumRevolutions int NumPoints = pointParCourbe * NumRevolution; //Dim oldPoint As New PointF( _ // ptOrigin.X + aRadius - bRadius + distance, ptOrigin.Y) PointF oldPoint = new PointF((ptOrigin.X + rayonA - rayonB + distance), ptOrigin.Y); //Dim angle As Double = 0 double angle = 0; //Dim aMinusb As Double = aRadius - bRadius double aMoinsB = rayonA - rayonB; //Dim aMinusbOverb As Double = aMinusb / bRadius double aDiviseB = aMoinsB / rayonB; //Dim pt As Integer //For pt = 0 To NumPoints - 1 // On fait le dessin.

for (int pt = 0; pt <= NumPoints; pt += 1) { angle += angleStep; PointF newPoint = new PointF((float)(ptOrigin.X + aMoinsB * Math.Cos(angle) + distance * Math.Cos(angle * aDiviseB)),(float)(ptOrigin.Y + aMoinsB * Math.Sin(angle) - distance * Math.Sin(angle * aDiviseB))); if (pt == 0) { oldPoint = newPoint; } if (random == false) { Pen Pinceau = new Pen(Color.FromArgb(rouge, vert, bleu), 1); dessin.DrawLine(Pinceau, oldPoint, newPoint); } else { Random r = new Random(); Pen Pinceau = new Pen(Color.FromArgb(r.Next(0, 256), r.Next(0, 256), r.Next(0, 256)), 1); dessin.DrawLine(Pinceau, oldPoint, newPoint); } oldPoint = newPoint; } dessin.Flush(); dessin.Dispose(); } 图片: 图片: 答 You cannot save bitmaps directly from the Graphics object of the Panel.First, you have to create a Bitmap object and derive

 Graphics from it.

Then, once the drawing is finished, ... Spirograph: correct wheel ratio and pen draw length? What is the ratio between the wheel size and the pen draw length in order to complete one turn, in a spirograph.

i.e a spirograph with :3 sides = 1.5 : 4pi (wheelratio : pen length)4 sides = 1.333 : 65 sides = 2.5 : 5 a)why do 1.2/10 and 6/2 both make a 6 side spirograph?a)What is the ratio?c)how do i make an octogon spirograph?function spiro ( N:float,k:int ): Vector3//spirograph loop, N=total points in loop, k=current loop { //wr,pr=wheel/pen ratio: 5, 3, 4, 6, 6, var wr:float[]=new float[10];wr[0]=2.5;wr[1]=1.5;wr[2]=1.33333;wr[3]=1.2;wr[4]=6; var pr:float[]=new float[10];pr[0]=5.0;pr[1]=4.0;pr[2]=6.00000;pr[3]=10; pr[4]=2; var vr =

 4; var wheel=wr[vr]; var theta =(1/N)*Mathf.PI *pr[vr]*k; var rtheta =theta*wheel; var small = (1-1/wheel);// var cx=Mathf.Cos(theta)*small; var cz=Mathf.Sin(theta)*small; var ex=Mathf.Cos(theta-rtheta)/wheel; var ez=Mathf.Sin(theta-rtheta)/wheel; return Vector3(cx+ex,0,cz+ez); } 图片: 图片: 图片: 答 There are some very nice pictures on the MathWorld articles on Spirographs and Hypotrochoids that make it much easier to picture what is happening.

Ad Hoc ExplanationFor a partic...

I'm trying to create a spirograph program which allows the user to input the angle used Using the code below I get the error : Traceback (most recent call last): File "E:\turtleTest2.py", line 4, in <module> x = input(int("Choose a number for the spirograph to use ")) ValueError: invalid literal for int() with base 10: 'Choose a number for the spirograph to use ' #TURTLES!!!2 import turtle x = input(int("Choose a number for the spirograph to use ")) def drawASquare(whichTurtle): for loopCounter in range(4): whichTurtle.forward(200) whichTurtle.right(x) window = turtle.Screen() timmy = turtle.Turtle() timmy.speed(0) colorCounter = 1 while True: drawASquare(timmy) timmy.left(2) if colorCounter == 1: timmy.color('blue') elif colorCounter == 2: timmy.color('red') elif colorCounter == 3: timmy.color('yellow') elif colorCounter == 4: timmy.color('green') colorCounter = 0 colorCounter += 1 I am doing this for a

 school side-project to learn more about Python programming.

Any help would be appreciated, thanks! 图片: 答 You've got the calls to the built-ins backwards. It should be like this:x = int(input("Choose a number for the spirograph to use ")) The above code gets the input and then conver... Spirograph History The mathematician Bruno Abakanowicz invented the Spirograph between 1881 and 1900. It was used for calculating an area delimited by curves. Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the Sears catalog. An article describing how to make a Wondergraph drawing machine appeared in the Boys Mechanic publication in 1913. The Spirograph itself was developed by the British engineer Denys Fisher, who exhibited at the 1965 Nuremberg International Toy Fair. It was subsequently produced by his company. US distribution rights were acquired by Kenner, Inc., which introduced it to the United States market in 1966 and promoted it as a creative children's toy.

In 2013 the Spirograph brand was re-launched in the USA by Kahootz Toys and in Europe by Goldfish and Bison with products that returned to the use of the original gears and wheels. The modern products use removable putty in place of pins or are held down by hand to keep the stationary pieces in place on the paper. The Spirograph was a 2014 Toy of the Year finalist in 2 categories, almost 50 years after the toy was named Toy of the Year in 1967. Spirograph Operation The original US-released Spirograph consisted of two different-sized plastic rings, with gear teeth on both the inside and outside of their circumferences. They were pinned to a cardboard backing with pins, and any of several provided gearwheels, which had holes provided for a ballpoint pen to extend through them to an underlying paper writing surface. It could be spun around to make geometric shapes on the underlying paper medium. Later, the Super-Spirograph consisted of a set of plastic gears and other interlocking shape-segments such as rings, triangles, or straight bars. It has several sizes of gears and shapes, and all edges have teeth to engage any other piece.

For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings. Kenner also introduced Spirotot, Magnetic Spirograph, Spiroman and various refill sets. To use it, a sheet of paper is placed on a heavy cardboard backing, and one of the plastic pieces—known as a stator—is secured via pins or reusable adhesive to the paper and cardboard. Another plastic piece—called the rotor—is placed so that its teeth engage with those of the pinned piece. For example, a ring may be pinned to the paper and a small gear placed inside the ring. The number of arrangements possible by combining different gears is very large. The point of a pen is placed in one of the holes of the rotor. As the rotor is moved, the pen traces out a curve. The pen is used both to draw and to provide locomotive force; some practice is required before the Spirograph can be operated without disengaging the stator and rotor, particularly when using the holes close to the edge of the larger rotors.

More intricate and unusual-shaped patterns may be made through the use of both hands, one to draw and one to guide the pieces. It is possible to move several pieces in relation to each other (say, the triangle around the ring, with a circle "climbing" from the ring onto the triangle), but this requires concentration or even additional assistance from other artists. Spirograph Mathematical basis Consider a fixed outer circle of radius centered at the origin. A smaller inner circle of radius is rolling inside and is continuously tangent to it. will be assumed never to slip on (in a real Spirograph, teeth on both circles prevent such slippage). Now assume that a point lying somewhere inside is located a distance from 's center. This point corresponds to the pen-hole in the inner disk of a real Spirograph. Without loss of generality it can be assumed that at the initial moment the point was on the -axis. In order to find the trajectory created by a Spirograph, follow point as the inner circle is set in motion. Now mark two points on and on . The point always indicates the location where the two circles are tangent. Point however will travel on and its initial location coincides with .

After setting in motion counterclockwise around , has a clockwise rotation with respect to its center. The distance that point traverses on is the same as that traversed by the tangent point on , due to the absence of slipping. Now define the new (relative) system of coordinates with its origin at the center of and its axes parallel to and . Let the parameter be the angle by which the tangent point rotates on and be the angle by which rotates (i.e. by which travels) in the relative system of coordinates. Because there is no slipping, the distances traveled by and along their respective circles must be the same, therefore or equivalently It is common to assume that a counterclockwise motion corresponds to a positive change of angle and a clockwise one to a negative change of angle. A minus sign in the above formula () accommodates this convention. Let be the coordinates of the center of in the absolute system of coordinates. Then represents the radius of the trajectory of the center of , which (again in the absolute system) undergoes circular motion thus: As defined above, is the angle of rotation in the new relative system.

Because point obeys the usual law of circular motion, its coordinates in the new relative coordinate system obey: In order to obtain the trajectory of in the absolute (old) system of coordinates, add these two motions: where is defined above. Now, use the relation between and as derived above to obtain equations describing the trajectory of point in terms of a single parameter : (using the fact that function is odd). It is convenient to represent the equation above in terms of the radius of and dimensionless parameters describing the structure of the Spirograph. Namely, let and The parameter represents how far the point is located from the center of . At the same time, represents how big the inner circle is with respect to the outer one . It is now observed that and therefore the trajectory equations take the form Parameter is a scaling parameter and does not affect the structure of the Spirograph. Different values of would yield similar Spirograph drawings. It is interesting to note that the two extreme cases and result in degenerate trajectories of the Spirograph. In the first extreme case when we have a simple circle of radius , corresponding to the case where has been shrunk into a point. (Division by in the formula is not a problem since both and are bounded functions).

The other extreme case corresponds to the inner circle 's radius matching the radius of the outer circle , ie . In this case the trajectory is a single point. Intuitively, is too large to roll inside the same-sized without slipping. If then the point is on the circumference of . In this case the trajectories are called hypocycloids and the equations above reduce to those for a hypocycloid. Spirograph Spirograph is a registered trademark of Hasbro, Inc., for a geometric drawing toy. The Spirograph produces mathematical curves of the variety technically known as hypotrochoids and epitrochoids. The term has also been used to describe a variety of software applications that display similar curves. The Spirograph was invented by British engineer Denys Fisher who exhibited it in 1965 at the Nuremberg International Toy Fair. It was subsequently produced by his company. Distribution rights were acquired by Kenner, Inc., which introduced it to the United States' market in 1966. A Spirograph consists of a set of plastic gears and other shapes such as rings, triangles, or straight bars. There are several sizes of gears and shapes, and all edges have teeth to engage any other piece.

For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings. To use it, a sheet of paper is placed on a heavy cardboard backing, and one of the plastic pieces is pinned to the paper and cardboard. Another plastic piece is placed so that its teeth engage with those of the pinned piece. For example, a ring may be pinned to the paper and a small gear placed inside the ring - the actual number of arrangements possible by combining different gears is very large. The point of a pen is placed in one of the holes in the moving piece. As the moving part is moved the pen traces out a curve. The pen is used both to draw and provide locomotive force; some practice is required before Spirograph can be operated without disengaging the fixed and moving pieces. More intricate and unusual-shaped patterns may be made through the use of both hands, one to draw and one to guide the pieces.

It is possible to move several pieces in relation to each other (say, the triangle around the ring, with a circle "climbing" from the ring onto the triangle), but this requires concentration or even additional assistance from other artists. Wikipedia contributors. Spirograph. Wikipedia, The Free Encyclopedia. October 8, 2008, 15:05 UTC. Available at: . Accessed November 24, 2008. What does spirograph mean? a geometric drawing toy consisting of a set of plastic gears and toothed rings Webster Dictionary(0.00 / 0 votes)Rate this definition: Spirograph(noun) an instrument for recording the respiratory movements, as the sphygmograph does those of the pulse Origin: [L. spirare to breathe + -graph.] Freebase(0.00 / 0 votes)Rate this definition: Spirograph A Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965.

"Spirograph" has also been used to describe a variety of software applications that display similar curves. It has also been applied to the class of curves that can be produced with the drawing equipment, and therefore may be regarded as a synonym of hypotrochoid. The name has been a registered trademark of Hasbro, Inc., since it bought the Denys Fisher company. Numerology The numerical value of spirograph in Chaldean Numerology is: 4 Pythagorean Numerology

Question: Which Denys Fisher geometric, plastic drawing toy produces mathematical curves of the variety technically known as hypotrochoids and epitrochoids?
Answer: Spirograph