Doing Mathematics with Tools: One Task, Four Tools

6533b836fe1ef96bd12a1bbd

RESEARCH PRODUCT

Doing Mathematics with Tools: One Task, Four Tools

subject

Engineering drawing Single task Straight edge Compass Protractor Task (project management)Angle bisector theorem Variety (cybernetics)

description

This chapter illustrates a variety of mathematical and educational issues arising from doing a single task with different tools. One task is considered, bisect an angle. The chapter has four sections, each devoted to issues in using one tool to complete this task: a straight edge and compass; a protractor; a dynamic geometry system; and a book.

year	journal	country	edition	language
2016-01-01

https://doi.org/10.1007/978-3-319-02396-0_2

PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
  - PE2_13Quantum optics and quantum information
  - PE2_15Thermodynamics
- PE1Mathematics
  - PE1_1Logic and foundations
  - PE1_6Geometry and global analysis
  - PE1_8Analysis
  - PE1_7Topology
  - PE1_9Operator algebras and functional analysis
  - PE1_10ODE and dynamical systems
  - PE1_12Mathematical physics
  - PE1_11Theoretical aspects of partial differential equations
  - PE1_13Probability
  - PE1_14Mathematical statistics
  - PE1_15Generic statistical methodology and modelling
  - PE1_4 Algebraic and complex geometry
  - PE1_19Scientific computing and data processing
  - PE1_2Algebra
  - PE1_20Control theory, optimisation and operational research
  - PE1_21Application of mathematics in sciences
  - PE1_22Application of mathematics in industry and society
  - PE1_5Lie groups, Lie algebras
  - PE1_18Numerical analysis
  - PE1_16Discrete mathematics and combinatorics
  - PE1_17Mathematical aspects of computer science
  - PE1_3Number theory
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  - PE3_1Structure of solids, material growth and characterisation
  - PE3_2Mechanical and acoustical properties of condensed matter, lattice dynamics
  - PE3_3Transport properties of condensed matter
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  - PE10_13Physical geography, geomorphology
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- PE11Materials Engineering
  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
  - PE11_4Engineering of polymers and plastics
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  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
- LS1Molecules of Life: Biological Mechanisms, Structures and Functions
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  - LS1_5Lipid biology
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  - LS1_11Chemical biology
  - LS1_12Protein design
  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
  - LS2_4Gene regulation
  - LS2_5Genomics
  - LS2_6Metagenomics
  - LS2_7Transcriptomics
  - LS2_8Proteomics
  - LS2_9Metabolomics
  - LS2_10Glycomics/Lipidomics
  - LS2_11Bioinformatics and computational biology
  - LS2_12Biostatistics
  - LS2_14Genetic diseases
  - LS2_16Innovative methods and modelling in integrative biology
  - LS2_13Systems biology
  - LS2_15Integrative biology for personalised medicine
- LS4Physiology in Health, Disease and Ageing
  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
  - LS4_6Microbiome and host physiology
  - LS4_7Nutrition and exercise physiology
  - LS4_8Impact of stress (including environmental stress) on physiology
  - LS4_9Metabolism and metabolic disorders, including diabetes and obesity
  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
  - LS4_12Cancer
  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
  - LS3_5Cell signalling and signal transduction, exosome biology
  - LS3_6Organelle biology and trafficking
  - LS3_7Mechanobiology of cells, tissues and organs
  - LS3_8Embryogenesis, pattern formation, morphogenesis
  - LS3_9Cell differentiation, formation of tissues and organs
  - LS3_10Developmental genetics
  - LS3_11Evolution of developmental strategies
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  - LS3_3Cell behaviour, including control of cell shape, cell migration
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  - LS3_14Regeneration
  - LS3_15Development of cell-based therapeutic approaches for tissue regeneration
  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
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  - LS3_1Cell cycle, cell division and growth
  - LS3_2Cell senescence, cell death, autophagy, cell ageing
- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
  - LS5_17Imaging in neuroscience
  - LS5_9Neural basis of cognition (e.g. learning, memory, attention, emotions, speech)
  - LS5_6Neurovascular biology and blood-brain barrier
  - LS5_8Neural basis of behaviour (e.g. sleep, consciousness, addiction)
  - LS5_4Neural stem cells
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- LS6Immunity, Infection and Immunotherapy
  - LS6_1Innate immunity
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SHSocial Sciences and Humanities
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