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Intuition and Logic in Mathematics. 数学中的直觉与逻辑。
Math Teacher Pub Date : 1900-01-01 DOI: 10.1017/cbo9781107252950.019
H. Poincaré
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引用次数: 35
A Description of The Department of Mathematics, The Royal Danish School of Educational Studies. 丹麦皇家教育研究学院数学系简介。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.3.0271
Bent Christiansen
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引用次数: 0
Use of Summation Operators for the Derivation of Common Formulae. 用求和算子求导一般公式。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.4.0296
R. Iman
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引用次数: 0
A Card Trick. 纸牌戏法。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.5.0395
C. W. Trigg
{"title":"A Card Trick.","authors":"C. W. Trigg","doi":"10.5951/mt.63.5.0395","DOIUrl":"https://doi.org/10.5951/mt.63.5.0395","url":null,"abstract":"Consider a standard deck of 52 cards stacked at the edge of a table. If you push the first one off the stack, how far will it go before it tips and falls on the floor? Half way, of course. Now lets start sliding the second one (and the first one). How far will those two go before they both fall? One-quarter card length. This gives a total overhang length of 1 2 + 1 4 = 3 4. Push the third card as far as it goes (one-sixth of a card length), and now the total overhang length will be 1 2 + 1 4 + 1 6 = 11 12. Can we ever push enough cards to make the total overhang length greater than one? At first glance it looks like 'no', but in fact the answer is yes, just push the fourth card! 1 2 + 1 4 + 1 6 + 1 8 = 25 24 ! How far will they go? What if we have more cards? All these answers lie in the following table: # Cards Pushed Overhang Length","PeriodicalId":144125,"journal":{"name":"Math Teacher","volume":"96 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":"114861318","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}
引用次数: 3
A Progress Report on the Implementation of the Recommendations of the Commission on Mathematics. 关于执行数学委员会各项建议的进度报告。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.6.0461
S. Williams
{"title":"A Progress Report on the Implementation of the Recommendations of the Commission on Mathematics.","authors":"S. Williams","doi":"10.5951/mt.63.6.0461","DOIUrl":"https://doi.org/10.5951/mt.63.6.0461","url":null,"abstract":"A LITTLE over ten years ago the Commission on Mathematics was formed by the College Board at the request of its Committee of Examiners in Mathemat ics. Although the Commission's primary concern has been the mathematics prepa ration of college-bound students, it has nevertheless been influential in shaping the efforts of the many groups of math ematicians and educators to reinvigorate the teaching of mathematics throughout the schools. In 1959 the Commission published its Program for College Preparatory Math ematics, in which it recommended the following nine-point program for students who are capable of doing college-level work:","PeriodicalId":144125,"journal":{"name":"Math Teacher","volume":"15 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":"126972986","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}
引用次数: 2
The Special Case May be the Hardest Part. 特殊情况可能是最难的部分。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.3.0249
Richard B. Thompson
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引用次数: 0
The Parallel Postulate. 平行假设。
Math Teacher Pub Date : 1900-01-01 DOI: 10.1038/scientificamerican12041920-565
Raymond H. Rolwing, Maita Levine
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引用次数: 4
The Magic of a Square. 正方形的魔力。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.1.0005
H. T. Freitag, Arthur H. Freitag
{"title":"The Magic of a Square.","authors":"H. T. Freitag, Arthur H. Freitag","doi":"10.5951/mt.63.1.0005","DOIUrl":"https://doi.org/10.5951/mt.63.1.0005","url":null,"abstract":"A magic square! Each row, each col umn, and both diagonals contain numbers whose sum is 34, the \"magic number MN\" as we shall call it. In addition, the artist contrived to show the year in which he created the woodcut. The two numbers? taken in order?in the middle of the bot tom row give you 1514. How did he accomplish this? How did he find such obligingly interesting num bers? Durer's magic square, as far as we know, is the first one that appeared in the West. But the problem traces its origin back several millennia. In one of the oldest of the Chinese classics, the I-King, ap pears the so-called lo-shu, first seen in 2200 b.c. (see fig. 2). Legend says it was first seen by the Emperor Yu. It was reputed to have been engraved on the back of a divine tortoise on the bank of the Yellow River. This is a three-by-three square, whose magic number is 15.","PeriodicalId":144125,"journal":{"name":"Math Teacher","volume":"26 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":"122219533","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}
引用次数: 11
Quadrarcs, St. Peter's, and the Colosseum. 方阵，圣彼得大教堂和罗马斗兽场。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.3.0209
N. T. Gridgeman
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引用次数: 3
High School Mathematics Background of College Freshmen Before and After Sputnik. 人造卫星前后大学新生的高中数学背景。
Math Teacher Pub Date : 1900-01-01 DOI: 10.5951/mt.63.4.0339
H. Kruglak
{"title":"High School Mathematics Background of College Freshmen Before and After Sputnik.","authors":"H. Kruglak","doi":"10.5951/mt.63.4.0339","DOIUrl":"https://doi.org/10.5951/mt.63.4.0339","url":null,"abstract":"THE launching of Sputnik 1 stimulated numerous heated debates and reforms in the teaching of science and mathematics. There are few published studies which compare two generations of high school students with respect to mathematics background during this critical period. It seemed worthwhile to compare the patterns of high school courses taken by entering college freshmen in the period immediately preceding Sputnik and five years later. The problem was formulated as a null hypothesis:","PeriodicalId":144125,"journal":{"name":"Math Teacher","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":"133889593","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}
引用次数: 2
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