Pub Date : 2020-03-05DOI: 10.1007/1-4020-0613-6_21261
D. Freed
{"title":"Writer","authors":"D. Freed","doi":"10.1007/1-4020-0613-6_21261","DOIUrl":"https://doi.org/10.1007/1-4020-0613-6_21261","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126378726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-04DOI: 10.1515/9783035619348-010
David C Mohrmann
The amount of force between two objects depends upon how much mass each contains and the distance between their centers of mass. For example, an apple hanging from a tree branch will have less gravitational force acting on it than when it has fallen to Earth. The reason for this is because the center of mass of an apple, when it is hanging from a tree branch, is farther from the center of mass of Earth than when lying on the ground.
{"title":"Fallingwater","authors":"David C Mohrmann","doi":"10.1515/9783035619348-010","DOIUrl":"https://doi.org/10.1515/9783035619348-010","url":null,"abstract":"The amount of force between two objects depends upon how much mass each contains and the distance between their centers of mass. For example, an apple hanging from a tree branch will have less gravitational force acting on it than when it has fallen to Earth. The reason for this is because the center of mass of an apple, when it is hanging from a tree branch, is farther from the center of mass of Earth than when lying on the ground.","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134141943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1976-01-01DOI: 10.1515/9780824880279-015
A. Westall
{"title":"About the Author","authors":"A. Westall","doi":"10.1515/9780824880279-015","DOIUrl":"https://doi.org/10.1515/9780824880279-015","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1976-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134148956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thank You, Eric Andersen","authors":"","doi":"10.2307/j.ctv1gn3t4r.10","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.10","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"65 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114123440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D irk Huylebrouck’s article on Leonardo’s geometric ‘‘slip-up’’ is interesting (The Mathematical Intelligencer 34, No. 4 (2012), 15–20). In fact the discovery of Leonardo’s ‘‘false’’ polyhedron by Rinus Roelofs is a little sensation. But the conclusion, that this polyhedron is false and that Leonardo made a mistake, is doubtful, and probably false itself. The polyhedron is only false if we, the viewers, insist that thebasepolyhedron is the rhombi-cuboctahedron, that is, one of the 13 Archimedean solids. If the ‘‘pseudorhombi-cuboctahedron’’ (the so-called 14th Archimedean solid) is taken as base, then Leonardo’s polyhedron is correct and it corresponds to his own label. Any undergraduate student with some geometric intuition can deduce this solid from the rhombi-cuboctahedron. So it is very likely that Leonardo (or Pacioli or some other Renaissance artist) knew this ‘‘14th solid,’’ and that Leonardo constructed his (correct) polyhedron on purpose from this base. Why might Leonardo have done this? The answer is quite simple: Riddles and puzzles in paintings were common in the Renaissance and in later times. (Another famous Renaissance example is the enigmatic polyhedron in Albrecht Dürer’s ‘‘Melencolia’’ with the hidden golden section.) Leonardo may have constructed his correct polyhedron to confuse the viewer, and to make her or him think about geometry. He could not know that it would take 500 years until Rinus Roelofs ‘‘rediscovered’’ this polyhedron.
D . irk Huylebrouck关于达芬奇几何“失误”的文章很有趣(The Mathematical Intelligencer, 34, No. 4(2012)， 15-20)。事实上，列奥纳多的“假”多面体的发现是一个小小的轰动。但结论是，这个多面体是假的，达芬奇犯了一个错误，这是值得怀疑的，很可能本身就是假的。这个多面体只有在我们，观察者，坚持认为底多面体是菱形-立方体，即13个阿基米德固体之一的情况下，才是错误的。如果以“伪正方体”(所谓的第14阿基米德固体)为基底，那么列奥纳多的多面体是正确的，它与他自己的标签相对应。任何有几何直觉的本科生都能从菱形-立方面体中推断出这个固体。所以很有可能列奥纳多(或帕乔利或其他文艺复兴时期的艺术家)知道这个“第14个立体”，并且列奥纳多故意从这个基底构造了他的(正确的)多面体。为什么列奥纳多会这样做呢?答案很简单:绘画中的谜语和谜题在文艺复兴时期和后来的时代很常见。(文艺复兴时期另一个著名的例子是阿尔布雷希特·德 (Albrecht d rer)的《Melencolia》中神秘的多面体，其中隐藏着黄金分割。)列奥纳多可能构造了正确的多面体来迷惑观众，让他或她思考几何。他不可能知道，直到500年后，里努斯·洛夫斯才“重新发现”了这个多面体。
{"title":"An Exchange","authors":"Jörg, M., Wills, D. Huylebrouck","doi":"10.2307/j.ctv1gn3t4r.28","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.28","url":null,"abstract":"D irk Huylebrouck’s article on Leonardo’s geometric ‘‘slip-up’’ is interesting (The Mathematical Intelligencer 34, No. 4 (2012), 15–20). In fact the discovery of Leonardo’s ‘‘false’’ polyhedron by Rinus Roelofs is a little sensation. But the conclusion, that this polyhedron is false and that Leonardo made a mistake, is doubtful, and probably false itself. The polyhedron is only false if we, the viewers, insist that thebasepolyhedron is the rhombi-cuboctahedron, that is, one of the 13 Archimedean solids. If the ‘‘pseudorhombi-cuboctahedron’’ (the so-called 14th Archimedean solid) is taken as base, then Leonardo’s polyhedron is correct and it corresponds to his own label. Any undergraduate student with some geometric intuition can deduce this solid from the rhombi-cuboctahedron. So it is very likely that Leonardo (or Pacioli or some other Renaissance artist) knew this ‘‘14th solid,’’ and that Leonardo constructed his (correct) polyhedron on purpose from this base. Why might Leonardo have done this? The answer is quite simple: Riddles and puzzles in paintings were common in the Renaissance and in later times. (Another famous Renaissance example is the enigmatic polyhedron in Albrecht Dürer’s ‘‘Melencolia’’ with the hidden golden section.) Leonardo may have constructed his correct polyhedron to confuse the viewer, and to make her or him think about geometry. He could not know that it would take 500 years until Rinus Roelofs ‘‘rediscovered’’ this polyhedron.","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126458912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"“One Way to Look at Your Life Is to Ask ‘What Have I Done with My Breath?’”","authors":"","doi":"10.2307/j.ctv1gn3t4r.4","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.4","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133869856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"“Let Us Go Forth with Fear and Courage and Rage to Save the World.”","authors":"","doi":"10.2307/j.ctv1gn3t4r.36","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.36","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115546349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Three Years On","authors":"","doi":"10.2307/j.ctv1gn3t4r.41","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.41","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115102492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mean Temperature or A Lesson by Degrees","authors":"","doi":"10.2307/j.ctv1gn3t4r.29","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.29","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127185794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Psalm","authors":"Psalm Micah Farmer","doi":"10.2307/j.ctv1gn3t4r.43","DOIUrl":"https://doi.org/10.2307/j.ctv1gn3t4r.43","url":null,"abstract":"","PeriodicalId":174397,"journal":{"name":"Back to the Light","volume":"273 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126632858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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