{"created":"2023-06-20T14:25:36.308040+00:00","id":6706,"links":{},"metadata":{"_buckets":{"deposit":"259df613-9bb3-4cee-90ea-d6a3af95bde3"},"_deposit":{"created_by":16,"id":"6706","owners":[16],"pid":{"revision_id":0,"type":"depid","value":"6706"},"status":"published"},"_oai":{"id":"oai:aue.repo.nii.ac.jp:00006706","sets":["6:406:846"]},"author_link":["73953"],"item_3_alternative_title_1":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Case Study of Mathematical Inquiry on Locus of Incenter and Excenters of Triangle with Dynamic Geometry Software GeoGebra","subitem_alternative_title_language":"en"}]},"item_3_biblio_info_7":{"attribute_name":"書誌事項","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2018-03-31","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"125","bibliographicPageStart":"117","bibliographicVolumeNumber":"6","bibliographic_titles":[{"bibliographic_title":"教科開発学論集","bibliographic_titleLang":"ja"}]}]},"item_3_description_27":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_language":"en","subitem_description_type":"Other"}]},"item_3_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"三角形の3つの頂点のうち、2つの頂点を固定し、もう1つの頂点をある曲線上で動かしたとき、三角形の5心がどのような軌跡を描くかについては、古くから考察されてきた。しかし、内心や傍心については、特別な場合を除いては、軌跡が2次曲線などになることがないため、代数的な方法で軌跡を求めることは困難である。近年、動的幾何ソフトが発達し、軌跡を描くだけでなくその方程式も求められるようになってきたが、内心と傍心の軌跡の方程式を求めることはできない。本研究では、曲線上を動く点から内心や傍心への座標変換式を求め、その逆変換式を利用することで、軌跡の方程式を求めることに成功した。その座標変換式は複雑な形となるが、頂点が楕円や双曲線上を動く場合について考察することにより、内心と3つの傍心の間には美しい関係が存在することを明らかにした。その結果は、頂点が動く曲線の種類を問わず、普遍的なものである。本研究は、SSH校等で実施予定の「理数探究」向けの教材開発を目指すものである。","subitem_description_language":"ja","subitem_description_type":"Abstract"},{"subitem_description":"Many mathematicians have been studied what kind of locus of triangle centers draw when two vertices of triangle are fixed points and another vertex move on curves. Since the locus of incenter and excenters never become quadratic curves except for special cases, it was difficult to obtain the locus equations by algebraic methods. In recent years, we can draw locus with dynamic geometric software easily, but it is impossible to obtain locus equations of incenter and excenters. In this study, we find the coordinate transformation formula from the point moving on the curve to incenter and excenters. We obtain locus equations of incenter and excenters by using the inverse transformation formula. The coordinate transformation formulas are complicated. But, we find beautiful relationships between the incenter and excenters by considering the case that the vertex moves on ellipse or hyperbola. The results are universal, regardless of the type of curve the vertex moves.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_3_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"愛知教育大学大学院・静岡大学大学院教育学研究科共同教科開発学専攻（後期３年博士課程）","subitem_publisher_language":"ja"}]},"item_3_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA1262681X","subitem_source_identifier_type":"NCID"},{"subitem_source_identifier":"AA12912422","subitem_source_identifier_type":"NCID"}]},"item_3_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2187-7327","subitem_source_identifier_type":"PISSN"}]},"item_3_text_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"subitem_text_value":"教科開発学論集. 2018, 6, p. 117-125."}]},"item_3_text_26":{"attribute_name":"著者別名","attribute_value_mlt":[{"subitem_text_value":"オオニシ, トシヒロ"}]},"item_3_text_4":{"attribute_name":"著者(別言語)","attribute_value_mlt":[{"subitem_text_value":"Onishi, Toshihiro"}]},"item_3_version_type_14":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"大西, 俊弘","creatorNameLang":"ja"}],"nameIdentifiers":[{"nameIdentifier":"73953","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-06-28"}],"displaytype":"detail","filename":"kaihatsu6117125.pdf","filesize":[{"value":"5.1 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"kaihatsu6117125.pdf","url":"https://aue.repo.nii.ac.jp/record/6706/files/kaihatsu6117125.pdf"},"version_id":"411a8496-e0b6-4b51-9b79-dbd138508486"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"内心","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"傍心","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"軌跡","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"方程式","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"GeoGebra","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"incenter","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"excenter","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"locus equation","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"三角形の内心・傍心の軌跡に関するテクノロジーを利用した数学的探究の実際－動的幾何ソフトGeoGebraを利用して－","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"三角形の内心・傍心の軌跡に関するテクノロジーを利用した数学的探究の実際－動的幾何ソフトGeoGebraを利用して－","subitem_title_language":"ja"}]},"item_type_id":"3","owner":"16","path":["846"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2018-06-28"},"publish_date":"2018-06-28","publish_status":"0","recid":"6706","relation_version_is_last":true,"title":["三角形の内心・傍心の軌跡に関するテクノロジーを利用した数学的探究の実際－動的幾何ソフトGeoGebraを利用して－"],"weko_creator_id":"16","weko_shared_id":-1},"updated":"2024-09-04T01:07:44.058331+00:00"}