Featured Research

from universities, journals, and other organizations

The Mathematics Of A Lampshade

Date:
June 7, 2001
Source:
Netherlands Organization For Scientific Research
Summary:
Try to solve the following maths problem: does x^3+y^2+1 produce the same form as x^3+3y^2+xy^2? For cubic equations, it’s possible to solve this problem, but mathematicians found things more difficult in the case of equations of the fourth order such as x^4+y^3+2y^2=3, a curve shaped like a lampshade. Eindhoven NWO researchers, funded by NWO Exact Sciences, have now found a method of dealing with equations of this type.

Try to solve the following maths problem: does x^3+y^2+1 produce the same form as x^3+3y^2+xy^2? For cubic equations, it’s possible to solve this problem, but mathematicians found things more difficult in the case of equations of the fourth order such as x^4+y^3+2y^2=3, a curve shaped like a lampshade. Eindhoven NWO researchers, funded by NWO Exact Sciences, have now found a method of dealing with equations of this type.

Related Articles


As part of an NWO project at Eindhoven University of Technology (TUE), mathematicians considered whether two different equations produced the same graph. In other words, are the two equations equivalent? They managed to solve this problem for fourth-order equations. The method also works for more complex fifth-order equations. The team first converted the fourth-order equations into quadratic equations, using so-called covariant mapping. Information is lost by doing this, but the resulting quadratic equations are easy to comprehend and to solve.

The team then used the solution to the quadratic equations to cancel out part of the original fourth-order equations. The remaining equations can then be solved with a bit of calculation. This new method can be used for equations of the fourth order and –with some modifications– for those of the fifth order. The Eindhoven team intend going on to see whether sixth-order or even more complex equations can be solved in the same way.

The problem of equivalence plays a role in such things as computer recognition of images. A computer is not able to see, for example, that an actual lampshade shown in two different ways is in fact the same lampshade. If the computer can convert the two images into mathematical formulae, it can use the new calculation method to work out that they represent the same lampshade. However, that is still in the future. Computers find the first step difficult, namely converting the lampshade into a mathematical formula.


Story Source:

The above story is based on materials provided by Netherlands Organization For Scientific Research. Note: Materials may be edited for content and length.


Cite This Page:

Netherlands Organization For Scientific Research. "The Mathematics Of A Lampshade." ScienceDaily. ScienceDaily, 7 June 2001. <www.sciencedaily.com/releases/2001/06/010605072127.htm>.
Netherlands Organization For Scientific Research. (2001, June 7). The Mathematics Of A Lampshade. ScienceDaily. Retrieved October 30, 2014 from www.sciencedaily.com/releases/2001/06/010605072127.htm
Netherlands Organization For Scientific Research. "The Mathematics Of A Lampshade." ScienceDaily. www.sciencedaily.com/releases/2001/06/010605072127.htm (accessed October 30, 2014).

Share This



More Computers & Math News

Thursday, October 30, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Samsung's Incredible Shrinking Smartphone Profits

Samsung's Incredible Shrinking Smartphone Profits

Reuters - Business Video Online (Oct. 30, 2014) The world's top mobile maker is under severe pressure, delivering a 60 percent drop in Q3 profit as its handset business struggles. Turning it around may not prove easy, says Reuters' Jon Gordon. Video provided by Reuters
Powered by NewsLook.com
Ban On Wearable Cameras In Movie Theaters Surprises No One

Ban On Wearable Cameras In Movie Theaters Surprises No One

Newsy (Oct. 30, 2014) The Motion Picture Association of America and the National Association of Theatre Owners now prohibit wearable cameras such as Google Glass. Video provided by Newsy
Powered by NewsLook.com
Microsoft Launches Fitness Band After Accidental Reveal

Microsoft Launches Fitness Band After Accidental Reveal

Newsy (Oct. 30, 2014) Microsoft accidentally revealed its upcoming fitness band on Wednesday, so the company went ahead and announced it. Video provided by Newsy
Powered by NewsLook.com
Mind-Controlled Prosthetic Arm Restores Amputee Dexterity

Mind-Controlled Prosthetic Arm Restores Amputee Dexterity

Reuters - Innovations Video Online (Oct. 29, 2014) A Swedish amputee who became the first person to ever receive a brain controlled prosthetic arm is able to manipulate and handle delicate objects with an unprecedented level of dexterity. The device is connected directly to his bone, nerves and muscles, giving him the ability to control it with his thoughts. Matthew Stock reports. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:

Strange & Offbeat Stories


Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

    Environment News

    Technology News



    Save/Print:
    Share:

    Free Subscriptions


    Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

    Get Social & Mobile


    Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

    Have Feedback?


    Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
    Mobile: iPhone Android Web
    Follow: Facebook Twitter Google+
    Subscribe: RSS Feeds Email Newsletters
    Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins