Etymologie, Etimología, Étymologie, Etimologia, Etymology
UK Vereinigtes Königreich Großbritannien und Nordirland, Reino Unido de Gran Bretaña e Irlanda del Norte, Royaume-Uni de Grande-Bretagne et d'Irlande du Nord, Regno Unito di Gran Bretagna e Irlanda del Nord, United Kingdom of Great Britain and Northern Ireland
Geometrie, Geometría, Géométrie, Geometria, Geometry















Geometric Areas of Mathematics


Erstellt: 2011-11






Spirograph (W3)

Dt. "Spirograph" setzt sich zusammen aus griech. "speira" = dt. "Windung" (vgl. dt. "Spirale") und griech. "-graphía", griech. "gráphein" = dt. "einritzen", "schreiben".

Es gibt jedoch auch in der Medizin einen "Spirografen", der sich zusammensetzt aus lat. "spirare" = "blasen", "wehen", "atmen" und griech. "-graphía", griech. "gráphein" = dt. "einritzen", "schreiben". Dabei handelt es sich um die apparative Aufzeichnung der bei der Spirometrie gemessenen Atmungswerte.


Spirograph Art


The Math in “Laser Light Math”
Of special interest was the issue of graphing a family of mathematical curves in the roulette or spirograph domain with laser light. Consistent with the techniques of making roulette patterns, images created by the Laser Light Math system are constructed by mixing sine and cosine functions together at various frequencies, shapes, and amplitudes. Images created in this fashion find birth in the mathematical process of making “roulette” or “spirograph” curves.


John Bowers: A Lesson from Spirograph


The Spirograph Nebula

Created Feb 2, 2009 | Updated Jul 3, 2014

"IC 418" has the more common name: The "Spirograph Nebula", and it's easy to see why, thanks to the image provided by the Hubble Space Telescope. This unique planetary nebula, 2,000 light years distant in the small southern constellation of Lepus 'the Hare', looks like it has been designed using the educational toy!


Spirograph animations - Spirographs in motion - Added on 2005-04-18

Spirograph code in Ultrafractal developed by Ken Childress.





Inspirograph online




Super Spirograph


Sound of Design / Lab / 360°


Explanation: What is creating the strange texture of "IC 418"? Dubbed the "Spirograph Nebula" for its resemblance to drawings from a cyclical drawing tool, planetary nebula IC 418 shows patterns that are not well understood.


Roulettes (Spirograph Curves) - Mathematical analysis



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.


"Roulette": The curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of conics when rolled upon a line are sections of minimal surfaces (i.e., they yield minimal surfaces when revolved about the line) known as unduloids.



A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. The curves above correspond to values of a=0.1, 0.2, ..., 1.0


What is a Spirograph?

A Spirograph is a curve formed by rolling a circle inside or outside of another circle. The pen is placed at any point on the rolling circle. If the radius of fixed circle is R, the radius of moving circle is r, and the offset of the pen point in the moving circle is O, then the equations of the resulting curve is defined by:


How to do Spirograph

Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.

Engl. "Spirograph" taucht in der Literatur um das Jahr 1860 auf.

Erstellt: 2015-01



Uni Clark
Euclid's Elements



Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages.

I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive.

The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. I still have a lot to write in the guide sections and that will keep me busy for quite a while.

This edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate the diagrams. If you enable Java on your browser, then you'll be able to dynamically change the diagrams. In order to see how, please read Using the Geometry Applet before moving on to the Table of Contents.

Erstellt: 2012-01