Document (#39905)

Author

Knuth, D.E.

Title

Mathematical typography

Source

Bulletin of the American Mathematical Society. 1979, nos.1/2, S.337-372 [http://www.ams.org/bull/1979-01-02/S0273-0979-1979-14598-1/]

Year

1979

Abstract

Mathematics books and journals do not look as beautiful as they used to. It is not that their mathematical content is unsatisfactory, rather that the old and well-developed traditions of typesetting have become too expensive. Fortunately, it now appears that mathematics itself can be used to solve this problem. A first step in the solution is to devise a method for unambiguously specifying mathematical manuscripts in such a way that they can easily be manipulated by machines. Such languages, when properly designed, can be learned quickly by authors and their typists, yet manuscripts in this form will lead directly to high quality plates for the printer with little or no human intervention. A second step in the solution makes use of classical mathematics to design the shapes of the letters and symbols themselves. It is possible to give a rigorous definition of the exact shape of the letter "a", for example, in such a way that infinitely many styles (bold, extended, sans-serif, italic, etc.) are obtained from a single definition by changing only a few parameters. When the same is done for the other letters and symbols, we obtain a mathematical definition of type fonts, a definition that can be used on all machines both now and in the future. The main significance of this approach is that new symbols can readily be added in such a way that they are automatically consistent with the old ones. Of course it is necessary that the mathematically-defined letters be beautiful according to traditional notions of aesthetics. Given a sequence of points in the plane, what is the most pleasing curve that connects them? This question leads to interesting mathematics, and one solution based on a novel family of spline curves has produced excellent fonts of type in the author's preliminary experiments. We may conclude that a mathematical approach to the design of alphabets does not eliminate the artists who have been doing the job for so many years; on the contrary, it gives them an exciting new medium to work with.

Theme

Elektronisches Publizieren

Object

TeX

Similar documents (author)

1. Knuth, D.E.: ¬The TeXBook (1986) 6.19

   6.1935673 = sum of:
     6.1935673 = weight(author_txt:knuth in 2594) [ClassicSimilarity], result of:
       6.1935673 = fieldWeight in 2594, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.909708 = idf(docFreq=5, maxDocs=44421)
         0.625 = fieldNorm(doc=2594)
   

2. Knuth, D.E.: ¬The letter S (1980) 6.19

   6.1935673 = sum of:
     6.1935673 = weight(author_txt:knuth in 3903) [ClassicSimilarity], result of:
       6.1935673 = fieldWeight in 3903, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.909708 = idf(docFreq=5, maxDocs=44421)
         0.625 = fieldNorm(doc=3903)
   

3. Duffy, T.M.; Knuth, R.A.: Hypermedia and instruction : where is the match? (1990) 4.95

   4.954854 = sum of:
     4.954854 = weight(author_txt:knuth in 2346) [ClassicSimilarity], result of:
       4.954854 = fieldWeight in 2346, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.909708 = idf(docFreq=5, maxDocs=44421)
         0.5 = fieldNorm(doc=2346)
   

4. Knuth, R.A.; Bruch, T.A.: Results of the hypertext '89 design survey (1990) 4.95

   4.954854 = sum of:
     4.954854 = weight(author_txt:knuth in 4916) [ClassicSimilarity], result of:
       4.954854 = fieldWeight in 4916, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.909708 = idf(docFreq=5, maxDocs=44421)
         0.5 = fieldNorm(doc=4916)
   

Similar documents (content)

1. Schwartzman, S.: ¬The words of mathematics : an etymological dictionary of mathematical terms used in English ; a reference book describing the origins of over 1500 mathematical terms used in English, including a glossary that explains the historical and linguistic terms used in the book (1994) 0.19

   0.18910067 = sum of:
     0.18910067 = product of:
       0.78791946 = sum of:
         0.013013239 = weight(abstract_txt:this in 881) [ClassicSimilarity], result of:
           0.013013239 = score(doc=881,freq=2.0), product of:
             0.040790696 = queryWeight, product of:
               1.085325 = boost
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.015619363 = queryNorm
             0.31902468 = fieldWeight in 881, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
         0.01874344 = weight(abstract_txt:used in 881) [ClassicSimilarity], result of:
           0.01874344 = score(doc=881,freq=1.0), product of:
             0.059552614 = queryWeight, product of:
               1.1356913 = boost
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.015619363 = queryNorm
             0.3147375 = fieldWeight in 881, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
         0.026443534 = weight(abstract_txt:such in 881) [ClassicSimilarity], result of:
           0.026443534 = score(doc=881,freq=1.0), product of:
             0.082450606 = queryWeight, product of:
               1.5430365 = boost
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.015619363 = queryNorm
             0.3207197 = fieldWeight in 881, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
         0.024024084 = weight(abstract_txt:that in 881) [ClassicSimilarity], result of:
           0.024024084 = score(doc=881,freq=1.0), product of:
             0.10835683 = queryWeight, product of:
               2.9334166 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.015619363 = queryNorm
             0.22171268 = fieldWeight in 881, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
         0.33962187 = weight(abstract_txt:mathematics in 881) [ClassicSimilarity], result of:
           0.33962187 = score(doc=881,freq=3.0), product of:
             0.31352407 = queryWeight, product of:
               3.008948 = boost
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.015619363 = queryNorm
             1.0832402 = fieldWeight in 881, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
         0.3660733 = weight(abstract_txt:mathematical in 881) [ClassicSimilarity], result of:
           0.3660733 = score(doc=881,freq=3.0), product of:
             0.3550497 = queryWeight, product of:
               3.5799656 = boost
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.015619363 = queryNorm
             1.031048 = fieldWeight in 881, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.09375 = fieldNorm(doc=881)
       0.24 = coord(6/25)
   

2. Popescu, F.: ¬An approach to eponyms in mathematics (2009) 0.18

   0.18489052 = sum of:
     0.18489052 = product of:
       0.6603233 = sum of:
         0.0061344993 = weight(abstract_txt:this in 2119) [ClassicSimilarity], result of:
           0.0061344993 = score(doc=2119,freq=1.0), product of:
             0.040790696 = queryWeight, product of:
               1.085325 = boost
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.015619363 = queryNorm
             0.15038967 = fieldWeight in 2119, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.017671486 = weight(abstract_txt:used in 2119) [ClassicSimilarity], result of:
           0.017671486 = score(doc=2119,freq=2.0), product of:
             0.059552614 = queryWeight, product of:
               1.1356913 = boost
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.015619363 = queryNorm
             0.29673737 = fieldWeight in 2119, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.017384205 = weight(abstract_txt:they in 2119) [ClassicSimilarity], result of:
           0.017384205 = score(doc=2119,freq=1.0), product of:
             0.074216194 = queryWeight, product of:
               1.2678248 = boost
               3.7477977 = idf(docFreq=2845, maxDocs=44421)
               0.015619363 = queryNorm
             0.23423736 = fieldWeight in 2119, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.7477977 = idf(docFreq=2845, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.0249312 = weight(abstract_txt:such in 2119) [ClassicSimilarity], result of:
           0.0249312 = score(doc=2119,freq=2.0), product of:
             0.082450606 = queryWeight, product of:
               1.5430365 = boost
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.015619363 = queryNorm
             0.3023774 = fieldWeight in 2119, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.022650123 = weight(abstract_txt:that in 2119) [ClassicSimilarity], result of:
           0.022650123 = score(doc=2119,freq=2.0), product of:
             0.10835683 = queryWeight, product of:
               2.9334166 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.015619363 = queryNorm
             0.20903271 = fieldWeight in 2119, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.22641458 = weight(abstract_txt:mathematics in 2119) [ClassicSimilarity], result of:
           0.22641458 = score(doc=2119,freq=3.0), product of:
             0.31352407 = queryWeight, product of:
               3.008948 = boost
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.015619363 = queryNorm
             0.7221601 = fieldWeight in 2119, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
         0.34513724 = weight(abstract_txt:mathematical in 2119) [ClassicSimilarity], result of:
           0.34513724 = score(doc=2119,freq=6.0), product of:
             0.3550497 = queryWeight, product of:
               3.5799656 = boost
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.015619363 = queryNorm
             0.9720815 = fieldWeight in 2119, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.0625 = fieldNorm(doc=2119)
       0.28 = coord(7/25)
   

3. Gray, J.: Symbols and suggestions : Communication of mathematics in print (2001) 0.17

   0.16761765 = sum of:
     0.16761765 = product of:
       0.5986345 = sum of:
         0.010844365 = weight(abstract_txt:this in 6893) [ClassicSimilarity], result of:
           0.010844365 = score(doc=6893,freq=2.0), product of:
             0.040790696 = queryWeight, product of:
               1.085325 = boost
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.015619363 = queryNorm
             0.26585388 = fieldWeight in 6893, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.015619535 = weight(abstract_txt:used in 6893) [ClassicSimilarity], result of:
           0.015619535 = score(doc=6893,freq=1.0), product of:
             0.059552614 = queryWeight, product of:
               1.1356913 = boost
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.015619363 = queryNorm
             0.26228127 = fieldWeight in 6893, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.3572001 = idf(docFreq=4205, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.030731222 = weight(abstract_txt:they in 6893) [ClassicSimilarity], result of:
           0.030731222 = score(doc=6893,freq=2.0), product of:
             0.074216194 = queryWeight, product of:
               1.2678248 = boost
               3.7477977 = idf(docFreq=2845, maxDocs=44421)
               0.015619363 = queryNorm
             0.41407704 = fieldWeight in 6893, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.7477977 = idf(docFreq=2845, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.16187143 = weight(abstract_txt:symbols in 6893) [ClassicSimilarity], result of:
           0.16187143 = score(doc=6893,freq=1.0), product of:
             0.28307548 = queryWeight, product of:
               2.4760592 = boost
               7.319441 = idf(docFreq=79, maxDocs=44421)
               0.015619363 = queryNorm
             0.57183135 = fieldWeight in 6893, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.319441 = idf(docFreq=79, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.04004014 = weight(abstract_txt:that in 6893) [ClassicSimilarity], result of:
           0.04004014 = score(doc=6893,freq=4.0), product of:
             0.10835683 = queryWeight, product of:
               2.9334166 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.015619363 = queryNorm
             0.3695211 = fieldWeight in 6893, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.16340065 = weight(abstract_txt:mathematics in 6893) [ClassicSimilarity], result of:
           0.16340065 = score(doc=6893,freq=1.0), product of:
             0.31352407 = queryWeight, product of:
               3.008948 = boost
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.015619363 = queryNorm
             0.5211742 = fieldWeight in 6893, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
         0.1761271 = weight(abstract_txt:mathematical in 6893) [ClassicSimilarity], result of:
           0.1761271 = score(doc=6893,freq=1.0), product of:
             0.3550497 = queryWeight, product of:
               3.5799656 = boost
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.015619363 = queryNorm
             0.49606323 = fieldWeight in 6893, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.078125 = fieldNorm(doc=6893)
       0.28 = coord(7/25)
   

4. Stathopoulos, Y.; Baker, S.; Rei, M.; Teufel, S.: Variable typing : assigning meaning to variables in mathematical text (2018) 0.16

   0.15551013 = sum of:
     0.15551013 = product of:
       0.6479589 = sum of:
         0.007668124 = weight(abstract_txt:this in 432) [ClassicSimilarity], result of:
           0.007668124 = score(doc=432,freq=1.0), product of:
             0.040790696 = queryWeight, product of:
               1.085325 = boost
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.015619363 = queryNorm
             0.18798709 = fieldWeight in 432, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
         0.034238245 = weight(abstract_txt:type in 432) [ClassicSimilarity], result of:
           0.034238245 = score(doc=432,freq=1.0), product of:
             0.0877875 = queryWeight, product of:
               1.1258502 = boost
               4.992163 = idf(docFreq=819, maxDocs=44421)
               0.015619363 = queryNorm
             0.39001274 = fieldWeight in 432, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.992163 = idf(docFreq=819, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
         0.022036277 = weight(abstract_txt:such in 432) [ClassicSimilarity], result of:
           0.022036277 = score(doc=432,freq=1.0), product of:
             0.082450606 = queryWeight, product of:
               1.5430365 = boost
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.015619363 = queryNorm
             0.2672664 = fieldWeight in 432, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
         0.16187143 = weight(abstract_txt:symbols in 432) [ClassicSimilarity], result of:
           0.16187143 = score(doc=432,freq=1.0), product of:
             0.28307548 = queryWeight, product of:
               2.4760592 = boost
               7.319441 = idf(docFreq=79, maxDocs=44421)
               0.015619363 = queryNorm
             0.57183135 = fieldWeight in 432, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.319441 = idf(docFreq=79, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
         0.028312655 = weight(abstract_txt:that in 432) [ClassicSimilarity], result of:
           0.028312655 = score(doc=432,freq=2.0), product of:
             0.10835683 = queryWeight, product of:
               2.9334166 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.015619363 = queryNorm
             0.2612909 = fieldWeight in 432, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
         0.39383218 = weight(abstract_txt:mathematical in 432) [ClassicSimilarity], result of:
           0.39383218 = score(doc=432,freq=5.0), product of:
             0.3550497 = queryWeight, product of:
               3.5799656 = boost
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.015619363 = queryNorm
             1.1092311 = fieldWeight in 432, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.078125 = fieldNorm(doc=432)
       0.24 = coord(6/25)
   

5. Sperber, W.; Ion, P.D.F.: Content analysis and classification in mathematics (2011) 0.15

   0.15211967 = sum of:
     0.15211967 = product of:
       0.54328454 = sum of:
         0.07677497 = weight(abstract_txt:mathematically in 818) [ClassicSimilarity], result of:
           0.07677497 = score(doc=818,freq=1.0), product of:
             0.13851649 = queryWeight, product of:
               8.868255 = idf(docFreq=16, maxDocs=44421)
               0.015619363 = queryNorm
             0.5542659 = fieldWeight in 818, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.868255 = idf(docFreq=16, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.008675492 = weight(abstract_txt:this in 818) [ClassicSimilarity], result of:
           0.008675492 = score(doc=818,freq=2.0), product of:
             0.040790696 = queryWeight, product of:
               1.085325 = boost
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.015619363 = queryNorm
             0.21268311 = fieldWeight in 818, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4062347 = idf(docFreq=10885, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.04941962 = weight(abstract_txt:step in 818) [ClassicSimilarity], result of:
           0.04941962 = score(doc=818,freq=1.0), product of:
             0.1301062 = queryWeight, product of:
               1.370608 = boost
               6.0774503 = idf(docFreq=276, maxDocs=44421)
               0.015619363 = queryNorm
             0.37984064 = fieldWeight in 818, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.0774503 = idf(docFreq=276, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.017629022 = weight(abstract_txt:such in 818) [ClassicSimilarity], result of:
           0.017629022 = score(doc=818,freq=1.0), product of:
             0.082450606 = queryWeight, product of:
               1.5430365 = boost
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.015619363 = queryNorm
             0.21381313 = fieldWeight in 818, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.42101 = idf(docFreq=3945, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.016016055 = weight(abstract_txt:that in 818) [ClassicSimilarity], result of:
           0.016016055 = score(doc=818,freq=1.0), product of:
             0.10835683 = queryWeight, product of:
               2.9334166 = boost
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.015619363 = queryNorm
             0.14780845 = fieldWeight in 818, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.3649352 = idf(docFreq=11344, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.13072053 = weight(abstract_txt:mathematics in 818) [ClassicSimilarity], result of:
           0.13072053 = score(doc=818,freq=1.0), product of:
             0.31352407 = queryWeight, product of:
               3.008948 = boost
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.015619363 = queryNorm
             0.41693935 = fieldWeight in 818, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.6710296 = idf(docFreq=152, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
         0.24404886 = weight(abstract_txt:mathematical in 818) [ClassicSimilarity], result of:
           0.24404886 = score(doc=818,freq=3.0), product of:
             0.3550497 = queryWeight, product of:
               3.5799656 = boost
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.015619363 = queryNorm
             0.68736535 = fieldWeight in 818, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.3496094 = idf(docFreq=210, maxDocs=44421)
               0.0625 = fieldNorm(doc=818)
       0.28 = coord(7/25)