Skip to main content
SpringerLink
Log in

Synthesis of Problems for Shaded Area Geometry Reasoning

  • Conference paper
  • First Online:
Artificial Intelligence in Education (AIED 2017)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

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

  2. Boyd, C.J., et al.: Geometry (NJ Edition). Glencoe/McGraw-Hill, New York (2006)

    Google Scholar 

  3. CBSE, India (2012). http://cbse.nic.in/

  4. Chew, T.: Singapore Math Challenge (Grade 5+). Frank Schaffer Publications, Greensboro (2008)

    Google Scholar 

  5. Coxeter, H.: Introduction to Geometry. Wiley, Hoboken (1969)

    Google Scholar 

  6. Holt, R., Winston: Holt Geometry: Homework and Practice Workbook. Holt, Rinehart and Winston, Orlando (2007)

    Google Scholar 

  7. Jurgensen, R., Brown, R., Jurgensen, J.: Geometry. Houghton Mifflin Company, Boston (1988)

    Google Scholar 

  8. Larson, R., Boswell, L., Kanold, T., Stiff, L.: Geometry. McDougal Littel, Evanston (2007)

    Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sumit Gulwani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rupak Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Supratik Mukhopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61424-3

  • Online ISBN: 978-3-319-61425-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation