Planes for which the lines are the shortest paths between points

Ralph Alexander

doi:10.1215/ijm/1256048729

Password Forgot your password?

Show

Remember Email on this computer

Remember Password

Please wait...

No Project Euclid account? Create an account
or Sign in with your institutional credentials

We can help you reset your password using the email address linked to your Project Euclid account.

Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches. Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content. Contact customer_support@projecteuclid.org with any questions.
View Project Euclid Privacy Policy

All Fields are Required

* First Name

* Last/Family Name

* Email

* Password

Password Requirements: Minimum 8 characters, must include as least one uppercase, one lowercase letter, and one number or permitted symbol Valid Symbols for password:
~ Tilde
! Exclamation Mark
@ At sign
$ Dollar sign
^ Caret
( Opening Parenthesis
) Closing Parenthesis
_ Underscore
. Period

* Confirm Password

Please wait...

Web Account created successfully

Browse
Resources
About

Advanced Search

Home > Journals > Illinois J. Math. > Volume 22 > Issue 2 > Article

June 1978 Planes for which the lines are the shortest paths between points

Ralph Alexander

Author Affiliations +

Ralph Alexander¹
¹University of Illinois, Urbana, Illinois

Illinois J. Math. 22(2): 177-190 (June 1978). DOI: 10.1215/ijm/1256048729

ABOUT
FIRST PAGE
CITED BY
DOWNLOAD PAPER SAVE TO MY LIBRARY

PERSONAL SIGN IN
Full access may be available with your subscription

Password Forgot your password?

Show

Remember Email on this computer

Remember Password

No Project Euclid account? Create an account
or Sign in with your institutional credentials

PURCHASE SINGLE ARTICLE

This article is only available to subscribers. It is not available for individual sale.

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

DOWNLOAD NOW

This content is available for download via your institution's subscription. To access this item, please sign in to your personal account.

Password Forgot your password?

Show

Remember Email on this computer

Remember Password

No Project Euclid account? Create an account

My Library

You currently do not have any folders to save your paper to! Create a new folder below.

First Page PDF

Access the abstract

JOURNAL ARTICLE
14 PAGES

DOWNLOAD PDF + SAVE TO MY LIBRARY

GET CITATION

My Library

You currently do not have any folders to save your paper to! Create a new folder below.

Folder Name

Folder Description

< Previous Article

Next Article >

Illinois J. Math.

Vol.22 • No. 2 • June 1978

Duke University Press

Subscribe to Project Euclid

Receive erratum alerts for this article

Ralph Alexander "Planes for which the lines are the shortest paths between points," Illinois Journal of Mathematics, Illinois J. Math. 22(2), 177-190, (June 1978)

Include:

Citation Only

Citation & Abstract

Format:

RIS

EndNote

BibTex

Print Friendly Version (PDF)

Quick Links

Browse
Search
About
Accessibility
Sign in

Information for Librarians

Manage my account
Subscriptions and Access
Librarian tools
More Help

Information for Publishers

Manage my account

Contact & Support

Business Office
905 W. Main Street
Suite 18B
Durham, NC 27701 USA
Help | Contact Us

Connect

Browse
Resources
About

Help | Advanced Search

KEYWORDS/PHRASES

Keywords

Remove

+ Add another field

PUBLICATION TITLE:

All Titles

Choose Title(s)

PUBLICATION YEARS

Range

Single Year

Clear Form