Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Therefore two distinct plane figures on a piece of paper are congruent if they can be cut out and then matched up completely. Turning the paper over is permitted. In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects. *Two line segments are congruent if they have the same length.
*Two angles are congruent if they have the same measure. *Two circles are congruent if they have the same diameter. In this sense

A New Look at Civic Design: Park Systems in America

Matthew Skjonsberg

A New Look at Civic Design reflects on the nature of the various crises facing the very idea of democracy today, explicitly in relation to climate change - namely mass extinctions, water scarcity and overabundance, and in general widespread and increasing ecological, social, and economic inequity - characteristics of our era, known now as the Anthropocene. The research proposes that these crises share anthropocentric materialism as a root cause, as instrumentalized by military industrialism and extractive industries, and asks: How would cities look if water had rights? How would regions be organized if soil had rights? How does a nation change if political boundaries are made congruent with ecological boundaries? How does the world look if we create a 'charter of elements'? Taking as a point of entry the 'new' Charter of Athens - involving as it does making policy recommendations regarding the regional scale relations of rural and urban districts, and the various infrastructures relating these - the dissertation is framed within a paradigm of nonlinearity, emphasizing reversibility and optionality. In turn, what fields of knowledge are best suited to inform nonlinear design practice? The dissertation is developed as a response to this question, resulting in a proposal. The central topic of the research is about form with a civic design development narrative, through elicitive modeling (form determinants established by analogy and analysis) and the design of form with which to relate rural and urban districts now - in light of ongoing industrialization and rapid urbanization. The research identifies a 'new school of nonlinear design' through historic figures, discourses and events, inventorying the processes involved in both positive and negative examples, involving pedagogical traditions, disciplinary heuristics and interdisciplinary interactions - with the aim of evoking positive nonlinearity through practical design methods. Civic designers' innovative park systems provide an important precedent of positive nonlinearity in practice, illustrating how a 'new school of nonlinear design' contributes to a design culture for the expansion of 'living rights'. The original contribution made by the dissertation to this research theme is to reveal park systems as the civic designer's innovative formal device - in pedagogy, policy and practice - as evidenced by the archival materials revealed through first-hand research. A New Look at Civic Design proposes a theoretical alternative to urban design, based on the interrelated concepts of optionality, reversibility and life cycles. The thesis traces a new tradition in design, while involving some familiar figures, where references - including pedagogues Schurtze, Addams and Montessori as well as designers Olmsted, Geddes, and Wright - are associated with the use of the concepts, the heuristics, and the means of design and creation from other disciplinary spheres - for example music, with the notion of counterpoint - arriving at a critical appreciation of the neglected discipline of civic design, which this dissertation advocates as an important social and ecological counterpoint to urban design, its more explicitly commercial disciplinary successor. The framing of this new tradition represents an attempt to overcome the acknowledged destructive tendencies of linearity with the means of design and pedagogy: the disciplinary tradition of an interdisciplinary ambition.

EPFL2018

A New Look at Civic Design: Park Systems in America

Matthew Skjonsberg

EPFL2018

A New Look at Civic Design: Park Systems in America

The union of congruent cubes in three dimensions

A New Look at Civic Design: Park Systems in America

The union of congruent cubes in three dimensions