Trench Warfare Diagram

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trench warfare diagram and trench diagram world war i trench warfare 99 trench warfare diagram ww1.

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idea trench warfare diagram and 81.

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awesome trench warfare diagram or diagram of trench warfare 85 trench warfare diagram ww1.

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awesome trench warfare diagram for trench warfare temporary trenches were also built saps were temporary unmanned often dead end utility trenches dug out into no mans 32.

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beautiful trench warfare diagram and related post 38.

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elegant trench warfare diagram or diagram of trench warfare 22 trench warfare diagram worksheet.

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fresh trench warfare diagram and soldiers in a trench on the western front 37 trench warfare diagram worksheet.

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inspirational trench warfare diagram and trench warfare diagram 86 trench warfare diagram ww1.

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fresh trench warfare diagram or trench warfare 68 trench warfare diagram worksheet.

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new trench warfare diagram or notes for infantry officers on trench warfare military museum library 43.

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best of trench warfare diagram for trench warfare world war 1 trench warfare diagram 94.

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luxury trench warfare diagram and the great trench warfare battles of 27 trench warfare diagram ww1.

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elegant trench warfare diagram for a large french digging machine building trenches on the western front during world war i 61 trench warfare diagram ww1.

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amazing trench warfare diagram and first world war trench maps national library of maps ocean trench diagram trench warfare diagram 17 trench warfare diagram worksheet.

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amazing trench warfare diagram for trench warfare on the western front 68 trench warfare diagram ww1.

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new trench warfare diagram and world war 1 net ocean trench trench warfare 49.

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good trench warfare diagram and triple entente trench warfare diagram depicting the layout of a typical trench system on the western front 95 trench warfare diagram worksheet.

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good trench warfare diagram and the gallery for no mans land trench warfare 98.

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idea trench warfare diagram and trench 34.

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good trench warfare diagram and trench warfare world war i trench warfare 71.

The structure of this humble diagram was formally developed by the mathematician John Venn, but its roots go back as far as the 13th Century, and includes many stages of evolution dictated by a number of noted logicians and philosophers. The earliest indications of similar diagram theory came from the writer Ramon Llull, whos initial work would later inspire the German polymath Leibnez. Leibnez was exploring early ideas regarding computational sciences and diagrammatic reasoning, using a style of diagram that would eventually be formalized by another famous mathematician. This was Leonhard Euler, the creator of the Euler diagram.

Logician John Venn developed the Venn diagram in complement to Eulers concept. His diagram rules were more rigid than Eulers - each set must show its connection with all other sets within the union, even if no objects fall into this category. This is why Venn diagrams often only contain 2 or 3 sets, any more and the diagram can lose its symmetry and become overly complex. Venn made allowances for this by trading circles for ellipses and arcs, ensuring all connections are accounted for whilst maintaining the aesthetic of the diagram.

A Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them. Commonly a Venn diagram will compare two sets with each other. In such a case, two circles will be used to represent the two sets, and they are placed on the page in such a way as that there is an overlap between them. This overlap, known as the intersection, represents the connection between sets - if for example the sets are mammals and sea life, then the intersection will be marine mammals, e.g. dolphins or whales. Each set is taken to contain every instance possible of its class; everything outside the union of sets (union is the term for the combined scope of all sets and intersections) is implicitly not any of those things - not a mammal, does not live underwater, etc.

Euler diagrams are similar to Venn diagrams, in that both compare distinct sets using logical connections. Where they differ is that a Venn diagram is bound to show every possible intersection between sets, whether objects fall into that class or not; a Euler diagram only shows actually possible intersections within the given context. Sets can exist entirely within another, termed as a subset, or as a separate circle on the page without any connections - this is known as a disjoint. Furthering the example outlined previously, if a new set was introduced - birds - this would be shown as a circle entirely within the confines of the mammals set (but not overlapping sea life). A fourth set of trees would be a disjoint - a circle without any connections or intersections.

Usage for Venn diagrams has evolved somewhat since their inception. Both Euler and Venn diagrams were used to logically and visually frame a philosophical concept, taking phrases such as some of x is y, all of y is z and condensing that information into a diagram that can be summarized at a glance. They are used in, and indeed were formed as an extension of, set theory - a branch of mathematical logic that can describe objects relations through algebraic equation. Now the Venn diagram is so ubiquitous and well ingrained a concept that you can see its use far outside mathematical confines. The form is so recognizable that it can shown through mediums such as advertising or news broadcast and the meaning will immediately be understood. They are used extensively in teaching environments - their generic functionality can apply to any subject and focus on my facet of it. Whether creating a business presentation, collating marketing data, or just visualizing a strategic concept, the Venn diagram is a quick, functional, and effective way of exploring logical relationships within a context.

Other Collections of Trench Warfare Diagram

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