Article history: Received 24 October 2008 Received in revised form 2 July 2009 Accepted 15 July 2009 Available online 17 July 2009 Communicated by F.Y.L. Chin

A carpenter’s ruler is a ruler divided into pieces of different lengths which are hinged where the pieces meet, which makes it possible to fold the ruler. The carpenter’s ruler folding problem, originally posed by Hopcroft, Joseph and Whitesides, is to determine the smallest case (or interval on the line) into which the ruler fits when folded. The problem is known to be NP-complete. The best pr...

See Teresa dc Lauretis, 'Aesthetic and Feminist Theory: Rethinking Women's Cinema', New German Critique 34, Winter 1985, pp 154-175. Madame X, a harsh, pitiless beauty, the cruel, uncrowned ruler of the China Seas, launched an appeal to all women willing to exchange an everyday existence of almost unbearable boredom, though safe and easy, for a world of uncertainty and danger, but also full of ...

The aims of this study were to compare the maximum range of protrusion determined with a ruler with measurements made using a George Gauge (GG) and to validate the methods of measurement (ruler and GG) of the advancement established by mandibular protruding devices (MPDs), using cephalograms as the gold standard. The study comprised 77 patients (63 males, 14 females, mean age 54 years, range 31...

A softcopy quality ruler method was implemented for the International Imaging Industry Association (I3A) Camera Phone Image Quality (CPIQ) Initiative. This work extends ISO 20462 Part 3 by virtue of creating reference digital images of known subjective image quality, complimenting the hardcopy Standard Reference Stimuli (SRS). The softcopy ruler method was developed using images from a Canon EO...

We consider Golomb rulers and their construction. Common rulers feature marks at every unit measure, distances can often be measured with numerous pairs of marks. On Golomb rulers, for every distance there are at most two marks measuring it. The construction of optimal—with respect to shortest length for given number of marks or maximum number of marks for given length—is nontrivial, various pr...

same initial elements. For the case of m= 12 this results in a reduction by a factor of about 80 in the number ofcases examined. Samples at m = 13 and 14 indicate that this pruning method will yield an additional improvement factor of about 2.5 to 3 for each increase in m. Using a characteristic vector representation, the test for a repeated spacing is improved by a factor of m2/8 over the stra...

Understanding measurement units is critical to mathematics and science learning, but it is a topic that American students find difficult. In 3 studies, we investigated the challenges underlying this difficulty in kindergarten and second grade by comparing performance on different versions of a linear measurement task. Children measured crayons that were either aligned or shifted relative to the...

An understanding of measurement and units of measurement is important in mathematics and science. However, children in the United States perform very poorly on measurement items on standardized mathematics tests compared to students in other countries. We examine understanding of linear measurement and units of measurement in 2 grade students and carry out a training study aimed at improving th...

We examined understanding of linear measurement in 1st and 2nd graders from high-and low-SES families. Children made two kinds of errors on measuring objects not aligned with the beginning of the ruler reading off the number that corresponded to the rightmost edge of the object (common in low SES children) and counting the number of hatch marks that the length of the ruler encompasses (common i...