意味 | 例文 (2件) |
Parallel postulateとは 意味・読み方・使い方
追加できません
(登録数上限)
意味・対訳 内角αとβの角度の和が180°未満であれば、二つの直線は無限に伸ばせば同じ側で交わる。
「Parallel postulate」の部分一致の例文検索結果
該当件数 : 2件
I've stitched euclid's parallel postulate on to the surface.例文帳に追加
表面にユークリッド幾何学の平行線公準を縫いました - 映画・海外ドラマ英語字幕翻訳辞書
If a parallel relation with a common postulate exists, the sides, in horizontal direction, of the both business elements circumscribe.例文帳に追加
前提条件を共通にする並列関係があるときは、双方の水平方向の辺同士を外接する。 - 特許庁
-
履歴機能過去に調べた
単語を確認! -
語彙力診断診断回数が
増える! -
マイ単語帳便利な
学習機能付き! -
マイ例文帳文章で
単語を理解!
Wiktionary英語版での「Parallel postulate」の意味 |
parallel postulate
語源
From the reference to parallel lines in the definition as formulated below, following Scottish mathematician John Playfair; this wording leads to a convenient basic categorisation of Euclidean and non-Euclidean geometries. The original formulation in Euclid's Elements makes no mention of parallels.
名詞
parallel postulate (複数形 parallel postulates)
- (geometry) An axiom of Euclidean geometry equivalent to the statement that, given a straight line L and a point P not on the line, there exists exactly one straight line parallel to L that passes through P; a variant of this axiom, such that the number of lines parallel to L that pass through P may be zero or more than one.
- 1962, Mary Irene Solon, The Parallel Postulates of Non-Euclidean Geometry, The Pentagon: A Mathematics Magazine for Students, Volumes 22-25, page 28,
- Before we examine the particulars of the parallel postulates of Hyperbolic and Elliptical geometries, we must see their logic.
- 1969, John B. Fraleigh, Mainstreams of Mathematics, Addison-Wesley, page 95,
- The earliest known attempt to prove the parallel postulates from the other axioms was by Ptolemy in about 150 A.D.
- 1989 [1965], Walter Prenowitz, Meyer Jordan, Basic Concepts of Geometry, Ardsley House Publishers, page 28,
- 1998, David A. Singer, Geometry: Plane and Fancy, Springer, page 16,
- 2006, John Ratcliffe, Foundations of Hyperbolic Manifolds, Springer, page 7,
- 1962, Mary Irene Solon, The Parallel Postulates of Non-Euclidean Geometry, The Pentagon: A Mathematics Magazine for Students, Volumes 22-25, page 28,
使用する際の注意点
Equivalent formulations include:
- (From Euclid's Elements): If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
- (The triangle postulate): The sum of the angles in any triangle equals a straight angle.
- Numerous others listed at Parallel postulate#Equivalent properties on Wikipedia.
Variations can be classified as follows:[1]
- (elliptic parallel postulate): No straight line exists that is parallel to L and passes through P;
- (Euclidean parallel postulate): Exactly one straight line exists that is parallel to L and passes through P;
- (hyperbolic parallel postulate): At least two straight lines exist that are parallel to L and pass through P.
It is also possible to forego the postulate entirely, as is the case in absolute geometry.
Further reading
- Absolute geometry on Wikipedia.
- Non-Euclidean geometry on Wikipedia.
|
意味 | 例文 (2件) |
|
Parallel postulateのページの著作権
英和・和英辞典
情報提供元は
参加元一覧
にて確認できます。
Text is available under Creative Commons Attribution-ShareAlike (CC-BY-SA) and/or GNU Free Documentation License (GFDL). Weblio英和・和英辞典に掲載されている「Wiktionary英語版」の記事は、Wiktionaryのparallel postulate (改訂履歴)の記事を複製、再配布したものにあたり、Creative Commons Attribution-ShareAlike (CC-BY-SA)もしくはGNU Free Documentation Licenseというライセンスの下で提供されています。 |
ピン留めアイコンをクリックすると単語とその意味を画面の右側に残しておくことができます。 |
ログイン |
Weblio会員(無料)になると 検索履歴を保存できる! 語彙力診断の実施回数増加! |
「Parallel postulate」のお隣キーワード |
weblioのその他のサービス
ログイン |
Weblio会員(無料)になると 検索履歴を保存できる! 語彙力診断の実施回数増加! |