## 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.

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.

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 July 23, 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 July 23, 2014).

## More Computers & Math News

Wednesday, July 23, 2014

### Featured Research

from universities, journals, and other organizations

### Featured Videos

from AP, Reuters, AFP, and other news services

Robot Parking Valet Creates Stress-Free Travel

### Robot Parking Valet Creates Stress-Free Travel

AP (July 23, 2014) — 'Ray' the robotic parking valet at Dusseldorf Airport in Germany lets travelers to avoid the hassle of finding a parking spot before heading to the check-in desk. (July 23) Video provided by AP
AP Review: Amazon Fire Adds Spark to Smartphones

### AP Review: Amazon Fire Adds Spark to Smartphones

AP (July 22, 2014) — Amazon's new Fire phone uses tweaks to the Android operating system and some innovative features to set it apart from smartphones from the likes of Apple and Samsung. (July 22) Video provided by AP
Apple Roundup: Smartwatch, iPhone 6 Orders And A Backdoor

### Apple Roundup: Smartwatch, iPhone 6 Orders And A Backdoor

Newsy (July 22, 2014) — Patents, iPhone order and backdoors: there's a lot of Apple news coming out this week. Don't worry, we've got you covered. Video provided by Newsy
Google Plans To Speed Up Web Pages With New Image Format

### Google Plans To Speed Up Web Pages With New Image Format

Newsy (July 21, 2014) — Google is using compressed images in WebP format to help boost page loading times. The files are 25-to-34 percent smaller than PNGs and JPEGs. Video provided by Newsy

## 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:
from the past week

## In Other News

... from NewsDaily.com

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