“Auxiliary line”的意思、由来-开放百科全书

词条

Auxiliary line

释义

References
External links

An auxiliary line (or helping line) is an extra line needed to complete a proof in plane geometry.^[1] Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles.

As an example, a proof of the theorem on the sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing through the opposite vertex).^[2]

Although the adding of auxiliary constructs can often make a problem obvious, it's not at all obvious to discover the helpful construct among all the possibilities, and for this reason many prefer to use more systematic methods for the solution of geometric problems (such as the coordinate method, which requires much less ingenuity).

References

1. ^{{cite book | url=https://books.google.com/books?id=brXqptpHUMQC&pg=PA107&dq=Auxiliary+line&hl=en&sa=X&ei=5DTvUYSsMujOyAGp9YDYCQ&ved=0CC0Q6AEwAA#v=onepage&q=Auxiliary%20line&f=false | title=Geometry the Easy Way (Barron's E–Z) | publisher=Barron's Educational Series; 3rd edition | author=Leff, Lawrence S. | year=1997 | pages=107 | isbn=978-0764101106}}
2. ^{{cite book|title=Mathematical People: Profiles and Interviews|url=https://books.google.com/books?id=1eHqBgAAQBAJ&pg=PA15|isbn=978-1-4398-6517-0|pages=15–16}}

External links

http://www.cut-the-knot.org/Generalization/MenelausByEinstein.shtml On Einstein's opinion regarding proofs that use the introduction of additional constructs

1 : Geometry

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。