Space is significant: Difference between revisions
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[[Category:Ambiguities]] | [[Category:Ambiguities]] | ||
[[Category:Handwriting]] | |||
Empty space is often significant in mathematical notation, but it's easy to misinterpret, and hard to produce accurately. | Empty space is often significant in mathematical notation, but it's easy to misinterpret, and hard to produce accurately. | ||
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There's some evidence that people learning algebra use the spacing of symbols to deduce rules.<ref>[https://www.jstor.org/stable/30034809 Visual salience of Algebraic Transformations], David Kirshner and Thomas Awtry, Journal for Research in Mathematics Education.</ref> | There's some evidence that people learning algebra use the spacing of symbols to deduce rules.<ref>[https://www.jstor.org/stable/30034809 Visual salience of Algebraic Transformations], David Kirshner and Thomas Awtry, Journal for Research in Mathematics Education.</ref> | ||
Producing reliable spacing in handwriting is hard. | |||
==Examples== | ==Examples== | ||
Entries in a matrix are separated by empty space: | Entries in a matrix are separated by empty space<ref>[https://twitter.com/christianp/status/1444937081915068416 Tweet by Christian Lawson-Perfect]</ref>: | ||
\[ \begin{pmatrix} 1 & - 2 \\ 3 & - 4 \end{pmatrix} \] | \[ \begin{pmatrix} 1 & - 2 \\ 3 & - 4 \end{pmatrix} \] | ||
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Statements about a line are usually separated from the main expression by a large space. | Statements about a line are usually separated from the main expression by a large space. | ||
\[ 4 | \[ 4 \equiv 1 \mod 3 \] | ||
versus | versus | ||
\[ 4 | \[ 4 \equiv 1 \bmod 3\] | ||
<hr/> | <hr/> | ||
Latest revision as of 10:15, 4 October 2021
Empty space is often significant in mathematical notation, but it's easy to misinterpret, and hard to produce accurately.
TeX applies different amounts of spacing around symbols based on context. The ubiquity of TeX means that typeset expressions without this spacing look odd.
There's some evidence that people learning algebra use the spacing of symbols to deduce rules.[1]
Producing reliable spacing in handwriting is hard.
Examples
Entries in a matrix are separated by empty space[2]:
\[ \begin{pmatrix} 1 & - 2 \\ 3 & - 4 \end{pmatrix} \]
\[ \begin{pmatrix} 1-2 \\ 3 - 4 \end{pmatrix} \]
Statements about a line are usually separated from the main expression by a large space.
\[ 4 \equiv 1 \mod 3 \]
versus
\[ 4 \equiv 1 \bmod 3\]
Juxtaposing two fractions:
\[ \frac{1}{2} \frac{-3}{4} \]
\[ \frac{1-3}{2\, 4} \]
References
- ↑ Visual salience of Algebraic Transformations, David Kirshner and Thomas Awtry, Journal for Research in Mathematics Education.
- ↑ Tweet by Christian Lawson-Perfect
