About this paper:
Appears in: ICERI2009 Proceedings
Publication year: 2009
Pages: 1849-1859
ISBN: 978-84-613-2953-3
ISSN: 2340-1095
Conference name: 2nd International Conference of Education, Research and Innovation
Dates: 16-18 November, 2009
Location: Madrid, Spain
The Triangular Model (TM) and its extension the Rough Triangular Model (RTM) presented in this paper, is a new approach to support students to memories and to study complex time depending data.

The study of a lot of disciplines (e.g. history, politics, geology, archaeology) is often connected to temporal information. The nature of this information can be of different kinds and is often very complex. To help a student to understand time depending context, a visualisation is common usage. For time intervals, the most widely adopted representation is the linear model. This conventional line model is often used to visualise temporal information like the sequence of historical events. It displays time intervals (e.g. lifetime of a king) as finite linear segments in a one-dimensional space. In this classical concept, a temporal interval I is visualised by a segment that is bounded by a begin point I- and end point I+. But, if a lot of information with a complex topology or even incomplete data is displayed, it is quickly getting overcharged and confusing.
The Triangular Model (TM) constitutes an alternative to the limited linear model. It is based on the W-diagram introduced in [Z. Kulpa, 1979]. The basic concept of TM is the construction of two lines through the extremes of a linear time interval. For each time interval I, two straight lines (L1 and L2) are constructed, with L1 going through I-; L2 going through I+, and where the angle a1 = a2. The intersection of L1 and L2 is called the interval point I. The position of I in the two-dimensional space completely determines both, the beginning and end point of the interval. Considering that the begin I- and end point I+ of two simple intervals have three possible relations: smaller than (<), equal (=) and larger than (>). Then, according to Allen [J.F. Allen 1983], thirteen possible fine relationships between two intervals can be defined. Using TM [N. Van de Weghe 2002], these relations can be visualised. Each relation thereby corresponds to a specific Zone within TM. From that, it follows that the spreading of the interval points within the TM gives an easy overview about the complex topology of time information. The TM is readable just as a map, depending on where within the triangle the Interval point is situated, questions like the following ones can be answered easily. Which historical person has been living at the same time, before, after or during a specific event? Who has been a kid while another person was dying? Who have been living longest/ shortest, earliest/ latest within a specific period? If the TM is used aided by a computer, any time scale can be displayed within the model. With zooming in and out very short intervals of e.g. a few seconds can be visualised next to intervals comprising several years or even more.
As a lot of disciplines are faced by the circumstance, that their time information is imprecise, the TM has been extended to the RTM.The RTM follows the same principle as the TM but in contrast to the TM it is not displaying simple time intervals with exact beginning and ending, but intervals with open beginning and/ or open ending. The RTM displays time intervals with imprecise beginning and ending as a diamond. Size, position and shape of the diamond are giving information about the dimension of uncertainty, temporal classification and duration of an interval. RTM has been successfully applied to an archaeological case study [N. Van de Weghe 2007],
time intervals, temporal relations, triangular model, rough triangular.