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Synthesis of Problems for Shaded Area Geometry Reasoning

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Artificial Intelligence in Education (AIED 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10331))

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Abstract

A shaded area problem in high school geometry consists of a figure annotated with facts such as lengths of line segments or angle measures, and asks to compute the area of a shaded portion of the figure. We describe a technique to generate fresh figures for these problems. Given a figure, we describe a technique to automatically synthesize shaded area problems. We demonstrate the efficacy of our synthesis techniques by synthesizing problems from fresh figures as well as figures from a corpus of problems from high-school geometry textbooks.

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References

  1. Alvin, C., Gulwani, S., Majumdar, R., Mukhopadhyay, S.: Technical report: synthesis of problems for shaded area geometry reasoning (2017). http://hilltop.bradley.edu/~calvin/papers/aied-full.pdf

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Author information

Authors and Affiliations

  1. Bradley University, Peoria, IL, USA

    Chris Alvin

  2. Microsoft Research, Redmond, WA, USA

    Sumit Gulwani

  3. Max Planck Institute for Software Systems, Kaiserslautern, Germany

    Rupak Majumdar

  4. Louisiana State University, Baton Rouge, LA, USA

    Supratik Mukhopadhyay

Authors
  1. Chris Alvin
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  2. Sumit Gulwani
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  3. Rupak Majumdar
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  4. Supratik Mukhopadhyay
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Corresponding author

Correspondence to Chris Alvin .

Editor information

Editors and Affiliations

  1. Human-Centered Multimedia, University of Augsburg, Augsburg, Germany

    Elisabeth André

  2. University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Ryan Baker

  3. Department of Psychology, University of Memphis, Memphis, Tennessee, USA

    Xiangen Hu

  4. Ateneo de Manila University, Quezon City, Philippines

    Ma. Mercedes T. Rodrigo

  5. University of Sussex, Brighton, United Kingdom

    Benedict du Boulay

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© 2017 Springer International Publishing AG

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Cite this paper

Alvin, C., Gulwani, S., Majumdar, R., Mukhopadhyay, S. (2017). Synthesis of Problems for Shaded Area Geometry Reasoning. In: André, E., Baker, R., Hu, X., Rodrigo, M., du Boulay, B. (eds) Artificial Intelligence in Education. AIED 2017. Lecture Notes in Computer Science(), vol 10331. Springer, Cham. https://doi.org/10.1007/978-3-319-61425-0_39

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  • DOI: https://doi.org/10.1007/978-3-319-61425-0_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61424-3

  • Online ISBN: 978-3-319-61425-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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