デカルトの卵形線の内外分枝の非対称軸について

• 蛭子井 博孝

  阪大

書誌事項

タイトル別名

• On asymmetry axes of the Oval of Descartes
• デカルト ノ ランケイセン ノ ナイガイ ブン シ ノ ヒタイショウジク ニ ツイテ

抄録

We define the inner (+) and the outer (-) part of the Cartesian Oval as mr₁±nr₂ = kc on bipolar coordinates.<BR>We can consider on Minor axis (asymmetry axis) of the inner part of the Oval, and can define Major axis (asymmetry axis) of the outer part of the Oval. This major axis is a segment which connects the middle point O of symmetry axis and the point Fp on the oval, which is at the longest distance from the point O. Then, the length of major axis is ao (1 + e_L e_R) ^1/2 (where ao is a half of the length of the symmetry-axis, e_L, e_R are left and right eccentricity of the Oval, respectively.) And, we can say that Cardioid is the special case of Cartesian Oval. In this case, e_L and e_R are equal to 1 and the length of the major axis is ao 2^1/2.<BR>Moreover, we have found the following Lemma. [Lemma] Let bi be the length of Minor axis of the inner part of the Oval, let ai and ao be the half length of symmetry-axis of the inner and outer part, respectively. Let bo be the length of the Major axis of the outer part. Then, the following invariant holds. (bi/ai) ²+ (bo/ao) ²=2

収録刊行物

• 図学研究

  図学研究 34 (2), 13-17, 2000

  JAPAN SOCIETY FOR GRAPHIC SCIENCE

キーワード

• 卵形線
• 外分枝
• 長軸
• 短軸
• 計量不変式

詳細情報

• CRID: 1390001204635754368
• NII論文ID: 10004813661
• NII書誌ID: AN00125240
• DOI: 10.5989/jsgs.34.2_13
• ISSN: 18846106
• ISSN: 03875512
• NDL書誌ID: 5440408
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5440408
• 本文言語コード: ja
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可