Mathematics

Scale Drawings and Maps

Scale drawings and maps are representations of real-life objects or places in a smaller or larger size. They maintain the proportions and measurements of the original object or place, allowing for accurate representation. The scale of a drawing or map indicates the ratio between the measurements on the drawing and the actual measurements, enabling accurate interpretation and measurement.

Written by Perlego with AI-assistance

6 Key excerpts on "Scale Drawings and Maps"

Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
  • Inside Meditation
    eBook - ePub

    Inside Meditation

    In search of the unchanging nature within

    • (Author)
    • 2012(Publication Date)
    • Matador
      (Publisher)
    There are different dimensions to scale and we are most familiar with the scale of cartography, which is a two dimensional or linear scale. Cartography portrays the ratio between two points on a map to the real distance between the two corresponding points. Scale can be expressed numerically like 1:100,000 or verbally like one centimetre on the map equals one kilometre on the earth. A map on a large scale shows much more detail than a map on a small scale.
    Another very familiar scale is the musical scale or octave in which ascending and descending notes are arranged by the composer in a specific scheme of intervals to create a piece of music. In medicine the idea of scale is used to measure mental and physical developments using a graded series of tests. Scale in maths is the notation of a given number system. A ruler or other measuring device represents the idea of scale as well as a weighing device.
    The scale of architecture takes us into three dimensions and features the relationship between different dimensions of organized space and structures in their relationship to the viewer. The scale and size of buildings, not only impresses the viewer, but also creates different moods, which are the result of the total interaction of dimensions in space, underlying every element of the composition. A variety of artistic effects can be achieved by creating a perfect balance between the geometry, height and textures and the way natural light enters the building. A relatively small architectural structure viewed from the outside, can give a much larger impression and sense of spaciousness once one enters the building, depending on the structural layout and use of space.
    Grand scale structures like ancient temples and cathedrals often symbolize the power and social position of the person ordering its construction. Some of them intend to make us feel insignificant where others are supposed to create an image or feeling, which is understood not only by contemporaries but also by future societies and cultures.
  • Beginning Design Technology
    • Mike Christenson(Author)
    • 2015(Publication Date)
    • Routledge
      (Publisher)
    4 Operation The impact of scale on representation Representational and artifactual scales
    Most of the scaled representations we encounter in everyday life—maps are an obvious example—are produced in order to represent objects or spaces that are too large to reproduce at their full size. Understood in this way, scale is simply a matter of convenience, making it possible for us to manipulate (to take in our hands) something otherwise too large to hold. It is also true that under certain circumstances, for example in assembly or fabrication diagrams, representations may be produced at full scale or even at scales larger than full scale. Maps are almost always drawn at scale, although in the well-known story “On exactitude in science,” Jorge Luis Borges tells a fantastic story about the map-as-territory:
    In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it.1
    In Borges’s story, the map represented the territory at a scale of 1:1. Every point in the territory was precisely reflected in the map; distances between points on the map equated precisely to the distances between corresponding points in the territory.2
    Like cartographers, architects also depend on scale to represent buildings, parts of buildings, building sites, neighborhoods, and cities, almost always at a size smaller than the thing-being-represented. For example, conventionally-produced architectural floor plans are usually drawn to a specific scale; physical models of buildings are also usually built at a specific scale. Maps or architectural plans may in theory be produced at any scale, but over time, conventional scales have developed, such as 1/4ʺ = 1′-0ʺ or 1:50 or 1:100 for architectural drawings, or 1:10,000 for maps.3 For several reasons, conventional scales are important whenever a map or plan is produced manually. First, conventional scales matter because the act of manually producing a map or plan at scale tends to rely on a limited set of generally available tools, such as straightedges or rulers calibrated into fixed, agreed-upon units. It is simply impractical to have more than a small set of conventional units (e.g., inches and centimeters). Second, conventional scales are important because the acts of sharing, exchanging, and comparing information are facilitated through the use of a common scale. Think, for example, of a collection of uniformly scaled maps such as the well-known USGS Quadrangle maps that make it easy to visually compare the relative sizes of territories or cities. Finally, the procedural difficulties involved in manually rescaling maps suggests that the number of different conventional scales should be kept to a minimum, and that these scales should be set in simple ratios to each other (for example, 1/2ʺ = 1ʹ-0ʺ and 1/4ʺ = 1ʹ-0ʺ). Nonetheless, some manually operated tools for producing scaled drawings, such as simple pantographs, don’t rely on conventional scales. A manually operated pantograph (Figure 4.1
  • Mapping It Out
    eBook - ePub

    Mapping It Out

    Expository Cartography for the Humanities and Social Sciences

    Scale, Perspective, and Generalization MAPS ARE SCALE MODELS OF REALITY. THAT IS, THE map almost always is smaller than the space it represents. I say “almost” because the graphic representations of subatomic particles and chromosomes drawn by nuclear physicists and geneticists are indeed maps, in the broad sense of using visible marks to portray relative positions. At the other end of the spectrum of map scales are the astronomer’s star charts, which represent the space-time relationships of an expanding universe. Like the microscope and the telescope, the geographic map can be an instrument of observation and discovery. And like genetic maps and galactic maps, geographic maps model the sizes, distances, and relative locations of phenomena we believe are real. By allowing us to discover or impose structure, these cartographic models promote both understanding and communication. As a graphic interface between reality and the mind, the map presents a selective view of reality—selective in the space it portrays, the viewpoint it offers, the objects it includes, and the symbols it uses to represent these objects. The map author must must make choices in three main elements of this graphic interface: scale, projection, and symbolization. Scale refers to the degree of reduction and is commonly stated as a ratio of distance on the map to distance on the ground. Because the scale of most maps is in the range between 1:5,000 and 1:500,000,000, cartographic models require considerably more generalization and abstraction than, say, a model railroad, with a scale between 1:48 and 1:220. Projection refers to the mathematical transformation that assigns objects on a curved, three-dimensional surface to locations on a flat, two-dimensional plane. Map projection tends to distort scale, distance, and area, and the projection chosen can either serve or thwart the map author’s goals
  • Cartography
    eBook - ePub

    Cartography

    The Ideal and Its History

    Roughly contemporary maps of the same place will be readily understood to be quite different in their form, content, and context according to the degree of reduction indicated by their map scale. The truth of this deterministic relationship is demonstrated in many texts by the comparison of details, placed side by side, of the same area from maps at different map scales. For example, Daniel Dorling and David Fairbairn (1997, 39) compared two maps of Bern, at 1:25,000 and 1:100,000 ; Michael Goodchild (2015b, 1384, fig. 883) compared three of Madison, Wisconsin, at 1:24,000, 1:100,000, and 1:250,000 ; and Bill Rankin (2016, 31) compared three centered on Washington Island, Wisconsin, from 1:250,000 to 1:2,000,000. Such comparisons are effective because the maps from which details are taken are specifically selected to be largely similar in style, if not in their degree of detail. In each of these examples, the numerical ratios of the selected maps all fall within one order of magnitude of each other. 1 But even with like compared to like within a limited range of scalar difference, there is sufficient variation to imply that such comparisons are extensible to other maps with quite different numerical ratios. Map scale thus appears to be a legitimately universal measure of reduction and generalization from the world to the map. All map scholars rely on the relative categories of large, medium, and small scale to quickly and efficiently summarize the nature and character of any given map. Thus, large-scale maps are widely understood to be the product of surveying by engineers, while small-scale maps are understood to be based on data visualization by social scientists. In this respect, cartography seems to comprise at least two major dialects, of “surveying and mapping.” Yet such institutional distinctions have never been allowed to undermine the coherence of cartography as a single endeavor (see chapter 3)
  • Digital Sketching
    eBook - ePub

    Digital Sketching

    Computer-Aided Conceptual Design

    • John Bacus(Author)
    • 2020(Publication Date)
    • Wiley
      (Publisher)
    Figure 3.9 ).
    You might think about this in terms of degrees of freedom. In a traditional sketch, in pencil on paper, the scale of the drawing is fixed. You can't stretch the paper to make it bigger or smaller. In a digital system, however, you can zoom to any scale you want. Scale doesn't mean as much in a CAD system as it does on paper. You are perhaps accustomed to managing this with the odd abstractions of “model space” and “paper space.” Scale makes even less sense in a 3D modeling viewport. Tellingly, many of the earliest CAD systems were, in fact, completely unitless, relying on the user to define whatever measurement system they wished.
    Figure 3.9 :
    Understanding the proportions.
    The freedom of dynamically zooming in, out, and panning around in a drawing is not available when you are working on a piece of paper. You can look closer, of course, if you need to see some detail in the drawing, and this is the experience that the original designers of CAD systems were trying to simulate. But it can become quite challenging to retain your inner sense of the scale of things as you zoom around so be very careful about this while you're sketching digitally.
    Traditional architectural scales are something that likely was baked in your subconscious as a student. You know, if it is how you were trained, that a drawing at 1/8″ = 1′ scale has specific properties that help you judge size and distance in it without needing to resort to a measuring device. You become accustomed to judging distance intuitively at scales that you know. When you're sketching, this is critically important to understand. You need to be able to tell if there is enough room in your plan sketches, for example, to fit a staircase, or a doorway, or a bathroom. You need to be able to judge this without resorting to a ruler or some other measuring tool (Figure 3.10
  • Geography in the Primary School (Routledge Revivals)
    • John Bale(Author)
    • 2013(Publication Date)
    • Routledge
      (Publisher)
    1:2,500) Ordnance Survey maps of the locality. Measuring exercises, working out the length of streets, journey to school and to play, all reinforce the notion of scale. Measuring the distance of a curved road or meandering river may pose problems. These can be overcome – especially with older children at the junior level – by using a blank sheet of paper, marking on it distances along the road at periodic points and then comparing this to the linear scale accompanying the map (Figure 4.2). This requires great care for accurate results. The idea of progressively smaller scales can be developed in the well-resourced school by comparing the local 1 kilometre grid square on the 1:2,500 plan with the same square on the 1:10,000, 1:25,000 and 1:50,000 maps. Figure 3.2 Making map measurements along a curved line using a graphic scale bar Figure 3.3 Introduction to co-ordinates by a simple map of the classroom Location. Young children can learn the relative locations of objects by recording on a flat base the places where model buildings need to be replaced if the model is reassembled the next day. Putting the models back in the right places gives children practice in recording locations and in the simple construction of a map. The learning of grid coordinates in order to specify locations more precisely than simple verbal descriptions may be related to work in mathematics or developed as part of a course on mapping skills. An initial suggestion is to conceptualise the classroom as a series of rows and columns, each row being numbered and each column being lettered. Each desk then can be individually identified by indicating the letter of the column in which it is found first and the number of the row second. Hence, the desk shaded black in Figure 3.3 is located by reference B3 (not 3B). A useful reminder about learning references is that the pupil goes ‘in the house and up the stairs’ (i.e. along the bottom row and up the column to locate the desired point)