Skip to main content

Part of the book series: Classics in Mathematics ((CLASSICS))

  • 2906 Accesses

Abstract

If we throw a heavy convex polyhedron with arbitrary interior mass distribution onto a horizontal floor then it will come to rest in a stable position on one of its faces. That is there exists for an arbitrary point P lying in the interior of the convex polyhedron one face F (at least) with the following property: The perpendicular dropped from P onto the plane in which F lies has its foot in the interior of the face F. Give a purely geometrical proof free from mechanical considerations for the existence of the face F.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pólya, G., Szegö, G. (1989). Geometric Problems. In: Problems and Theorems in Analysis II. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61905-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-61905-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63686-1

  • Online ISBN: 978-3-642-61905-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics