refresh print


Measuring is an important part, perhaps even the origin, of geometry. Cinderella has modes for measuring distances, angles, and area. Their behavior, at least in Euclidean geometry, is relatively straightforward:

  • Select two points and obtain the distance between them.
  • Select two lines and obtain the angle between them.
  • Select a polygon, circle, or conic and obtain its area.

For most purposes that is all you have to know. However, as usual, there are many fine details that sometime make things more difficult. If you deal with non-Euclidean geometries, their crucial defining property is a strange way to measure things. What goes on exactly is described in more detail in the section Theoretical Background. For now, it is sufficient to know that in non-Euclidean geometries measurements differ from the usual Euclidean measurements. Values of distances or angles may even become complex numbers. These values can be calculated with the theory of Cayley-Klein geometries.

The treatment of measurements in such a general way is one of the core features of Cinderella. You should not worry about the strange behavior of measurement in non-Euclidean geometries. Perhaps the best way to understand it is to play with different constructions to get a feeling for its unique aspects. Allowing people to get an intuitive feel for non-Euclidean geometries is one of the main goals of Cinderella.

Another fine point comes from the measurements of areas. Cinderella is able to measure the area of polygons and conics. In both cases there are a few things that deserve some extra attention. It is easy to define the area for a polygon that does not intersect itself. But what happens if it does? The approach chosen in Cinderella is to use a general and consistent formula for area. Areas are counted with respect to an orientation. How much a point inside the polygon contributes to the area depends on its winding number with respect to the boundary.

The area of conics is also a delicate topic. It is easy to define the area of an ellipse. But what is the area of a hyperbola? Is it infinite? Is it undefined? Is it something completely different? Cinderella chooses an algebraic approach that tries to use only one formula for all the different cases. It turns out that the area of a hyperbola is most reasonably described by a complex number. So, if you make measurements of areas of conics do not be surprised if complex numbers sometimes show up.

In particular, the measurement modes are



The measurements are shown as texts. They can be used as "text objects," so they can be dragged around and be repositioned. Consult the description of text and function for these features.

Contributors to this page: Richter , Kortenkamp and Kramer .
Page last modified on Wednesday 27 of July, 2011 [12:48:56 UTC] by Richter.

The content on this page is licensed under the terms of the License.

free viagra samplehentai girlsmature pussymilfseeker cialis samplescam clip movie nude webcammother incest order viagra online cialis ukanime rapeparis hilton phone numbers viagra alternatives cialis forum cialis free samplehot girls in pantiesmonster of cocks discount cialis cilias free viagra samplesfree chat rooms cilia structurefree cartoon sex comics buy cialis order viagrafree adult videosplump girl gallerypantyhose gallerycum on her face cheapest cialisbisexual moviestampa bukakehuge black cock thumbnails buy cialis onlineporn star cialis drugwomen having sex cheap generic viagra alternative to viagra natural viagra cheap viagraoral sexteen webcam strip videosnude spanish girlserotic sex cams movies viagra side effectscartoon adultdisney sex animenude blonde hairygang bang swinger cialis viagrabisexual free moviesgay twinkswebcam chat live xxxyoung teens order cialislatina girls thongscum loversjapanese girl viagra cheapyoung japanese girlsmr chews asian beavergangbang squadshoshone indiansmature wiveslive webcam chat girlsfree ebony viagra on lineasian ladyboysteen boys viagra pillsself bondage techniques cailisincest familyfree ebony cheap cialisgay amateur cialis genericbusty asian viagra onlinemature breasts viagra for women free viagrabig boobies cialis generic viagragloryhole gaylatinas in thongs female viagraindian tits viagra 6 free samplesamateur upskirt viagra alternativefree xxx video cialis online discountgalleries of teen girls cialis dosage cheap generic cialisparis hilton pornopussy cat dollsbrutal sexgay peopleblack milfsno tits discount viagrablonde hairy pussyshemale animefree hardcore moviesmom strips for sonfat titscelebrity legsdouble anal levitra vs cialis cialis tadalafil cialis cheapgay bdsmcelebrities exposed viagra generic alternatives to viagra viagra canadabestialitypink porn stars viagra jokesclips of teen sexchicks suck horse cock online viagrasex with horsespainful analglory holes floridafree american bukkake cialis online buy viagrabig cock cum free cialisteen gay porn cialis side effects herbal viagra best price viagra purchase cialis cialis soft tabs cialis vs viagrafree fat girl webcamfree porn movie clipsoral penis suckingebony hardcore viagra pricepantyhose crossed legs cialis and levitralesbiennesblonde boobs buy viagra online