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authordakkar <dakkar@thenautilus.net>2011-05-23 20:53:57 +0100
committerdakkar <dakkar@thenautilus.net>2011-05-23 20:54:16 +0100
commita0cfe8c3ae74681335d9f004c65946fa4141b1a6 (patch)
tree66f699fb74fa28cd176ec00df43c4801ab0d028f
parentupdated anime page (diff)
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new page: slide rules
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+===========================
+Log-scale calculation tools
+===========================
+:CreationDate: 2011-05-23 18:46:11
+:Id: HW/logscale-calc-tools
+:tags: - hardware
+ - vintage
+
+Uh? What?
+=========
+
+Maybe you know better the name "slide rules". Or maybe not even that
+one… Short version: ``log(x*y) = log(x)+log(y)``, so if you have a
+pair of rulers with a logarithmic scale, you can use them to perform
+multiplications and divisions. More details on dedicated sites, like
+`Ron Manley's one <http://www.sliderule.ca/>`_ o `Eric Marcotte's one
+<http://www.sliderules.info/>`_.
+
+All right, let's pretend we've understood that…
+===============================================
+
+I have here a classic slide rule, and a cylindrical slide "rule" (of
+the `Otis King <http://en.wikipedia.org/wiki/Otis_King>`_ variety). I
+want to show how to perform a couple of simple operations.
+
+Multiplication
+==============
+
+We want to multiply 7 by 3. Easy, right?
+
+Let's start with the slide rule:
+
+1) make 1 on the C scale match with 7 on the D scale
+
+ .. image:: s7x3-1.jpg
+ :alt: 1 on C scale matching with 7 on D scale
+
+2) look with what, on the D scale, matches 3 on the C scale
+
+ .. image:: s7x3-2.jpg
+ :alt: 3 on C scale matching with 21 on D scale
+
+ 21, which is our result [1]_
+
+With the cylindrical rule things are a bit more awkward.
+
+1) point to 1 on the lower scale, with the cursor
+
+ .. image:: r7x3-2.jpg
+ :alt: cursor pointing to 1 on lower scale
+
+2) point 7 on the upper scale, *moving only this scale*
+
+ .. image:: r7x3-1.jpg
+ :alt: cursor pointing to 7 on upper scale
+
+3) now move *only the cursor*, making it point to 3 on the lower scale
+
+ .. image:: r7x3-3.jpg
+ :alt: cursor pointing to 3 on lower scale
+
+4) on the upper scale we read our result
+
+ .. image:: r7x3-4.jpg
+ :alt: cursor pointing to 21 on upper scale
+
+It's totally equivalent to the linear rule: the two logarithmic scales
+are equal, so a translation on one, "sums" to the other.
+
+Division
+========
+
+Let's divide 24 by 4.
+
+Linear rule:
+
+1) make 4 on the C scale match with 24 on the D scale
+
+ .. image:: s24d4-1.jpg
+ :alt: 4 on C scale matching with 24 on D scale
+
+2) look with what, on the D scale, matches 1 on the C scale
+
+ .. image:: s24d4-2.jpg
+ :alt: 1 on C scale matching 6 on D scale
+
+ 6, again our result.
+
+Cylindrical rule:
+
+1) point to 4 on the lower scale, with the cursor
+
+ .. image:: r24d4-2.jpg
+ :alt: cursor pointing to 4 on lower scale
+
+2) point 24 on the upper scale, *moving only this scale*
+
+ .. image:: r24d4-1.jpg
+ :alt: cursor pointing to 24 on upper scale
+
+3) now move *only the cursor*, making it point to 1 on the lower scale
+
+ .. image:: r24d4-3.jpg
+ :alt: cursor pointing to 1 on lower scale
+
+4) on the upper scale we read our result [2]_
+
+ .. image:: r24d4-4.jpg
+ :alt: cursor pointing to 6 on upper scale
+
+Some notes
+==========
+
+The advantage of the cylindrical rule is that it allows longer scales
+in a small space; the longer the scale, the more precise you can be in
+reading it.
+
+The advantages of the linear rule are in the ease of use, and in the
+simplicity of concatenating operations one after the one, especially
+when using more than 2 scales (the slide rule you see above has 6
+scales: two regular ones, two quadratic, one reciprocal, one cubic).
+
+.. [1] OK, I cheated a bit, since at first glance you'd think of using
+ the other 1 on the C scale (the one on the left hand side), but
+ if you try that, the 3 on C ends up out of the rule; the trick
+ works because it's equivalent to:
+
+ * divide 7 by 10 (10C:7D → 1C:7D (this 7 is outside the rule,
+ on the left hand side))
+ * multiply that by 3
+
+ or, if you prefer, 7CI:1D 3C:21D (using the reciprocal scale).
+
+.. [2] just as in the multiplication with the linear rule, here too we
+ are reading on the "wrong side" of the scale; it works for the
+ same reason.
diff --git a/src/HW/logscale-calc-tools/document.it.rest.txt b/src/HW/logscale-calc-tools/document.it.rest.txt
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+=============================================
+Strumenti per il calcolo in scala logaritmica
+=============================================
+:CreationDate: 2011-05-23 18:46:11
+:Id: HW/logscale-calc-tools
+:tags: - hardware
+ - vintage
+
+Eh? Che hai detto?
+==================
+
+Forse avete più familiare il nome "regoli calcolatori". O magari
+neppure questo… Versione breve: ``log(x*y) = log(x)+log(y)``,
+per cui se avete un paio di righelli in scala logaritmica, potete
+usarli per fare moltiplicazioni e divisioni. Maggiori dettagli presso
+siti specializzati, quali `quello di Ron Manley
+<http://www.sliderule.ca/>`_ o `quello di Eric Marcotte
+<http://www.sliderules.info/>`_.
+
+Va be', facciamo finta di aver capito…
+======================================
+
+Ho sotto mano un regolo "classico", e un regolo cilindrico (tipo `Otis
+King <http://en.wikipedia.org/wiki/Otis_King>`_). Voglio mostrare un
+paio di semplici operazioni.
+
+Moltiplicazione
+===============
+
+Vogliamo moltiplicare 7 per 3. Facile, vero?
+
+Cominciamo col regolo lineare:
+
+1) facciamo corrispondere 1 della scala C con 7 della scala D
+
+ .. image:: s7x3-1.jpg
+ :alt: 1 della scala C corrispondente a 7 della scala D
+
+2) guardiamo a cosa, sulla scala D, corrisponde il 3 della scala C
+
+ .. image:: s7x3-2.jpg
+ :alt: 3 della scala C corrisponde a 21 della scala D
+
+ 21, ovvero il nostro risultato [1]_
+
+Col regolo cilindrico è un po' meno ovvio.
+
+1) puntiamo 1 sulla scala inferiore, col cursore
+
+ .. image:: r7x3-2.jpg
+ :alt: cursore che punta 1 sulla scala inferiore
+
+2) puntiamo 7 sulla scala superiore, *muovendo solo quest'ultima*
+
+ .. image:: r7x3-1.jpg
+ :alt: cursore che punta 7 sulla scala superiore
+
+3) ora portiamo il cursore sul 3 della scala inferiore, *muovendo solo
+ il cursore*
+
+ .. image:: r7x3-3.jpg
+ :alt: cursore che punta 3 sulla scala inferiore
+
+4) sulla scala superiore si legge il risultato
+
+ .. image:: r7x3-4.jpg
+ :alt: cursore che punta 21 sulla scala superiore
+
+È del tutto equivalente al regolo lineare: le due scale logaritmiche
+sono uguali, per cui una traslazione su una, "somma" all'altra.
+
+Divisione
+=========
+
+Dividiamo 24 per 4.
+
+Regolo lineare:
+
+1) facciamo corrispondere 4 della scala C con 24 della scala D
+
+ .. image:: s24d4-1.jpg
+ :alt: 4 della scala C corrispondente a 24 della scala D
+
+2) guardiamo a cosa, sulla scala D, corrisponde 1 della scala C
+
+ .. image:: s24d4-2.jpg
+ :alt: 1 della scala C corrisponde a 6 della scala D
+
+ 6, ovvero il nostro risultato.
+
+Regolo cilindrico:
+
+1) puntiamo 4 sulla scala inferiore, col cursore
+
+ .. image:: r24d4-2.jpg
+ :alt: cursore che punta 4 sulla scala inferiore
+
+2) puntiamo 24 sulla scala superiore, *muovendo solo quest'ultima*
+
+ .. image:: r24d4-1.jpg
+ :alt: cursore che punta 24 sulla scala superiore
+
+3) ora portiamo il cursore sul 1 della scala inferiore, *muovendo solo
+ il cursore*
+
+ .. image:: r24d4-3.jpg
+ :alt: cursore che punta 1 sulla scala inferiore
+
+4) sulla scala superiore si legge il risultato [2]_
+
+ .. image:: r24d4-4.jpg
+ :alt: cursore che punta 6 sulla scala superiore
+
+Note varie
+==========
+
+Il vantaggio del regolo cilindrico è che permette di avere scale molto
+lunghe in poco spazio: più lunga è la scala, più precise sono le
+letture.
+
+I vantaggi del regolo lineare stanno nella facilità d'uso e nella
+comodità di incastrare più operazioni una dopo l'altra, specie avendo
+più di 2 scale (il regolo lineare che vedete sopra ha 6 scale: due
+normali, due quadratiche, una inversa, una cubica).
+
+.. [1] OK, ho un po' truccato, in quanto di primo acchito verrebbe da
+ usare l'altro 1 della scala C (quello a sinistra), ma in quel
+ modo il 3 di C finisce fuori dal regolo; il trucco funziona
+ perché è equivalente a:
+
+ * dividere 7 per 10 (10C:7D → 1C:7D (questo 7 è fuori dal
+ regolo, dal lato sinistro))
+ * moltiplicare quello per 3
+
+ o, se preferite, 7CI:1D 3C:21D (usando la scala reciproca).
+
+.. [2] come per la moltiplicazione col regolo lineare, pure qua stiamo
+ leggendo "dal lato sbagliato" della scala; il tutto funziona
+ per gli stessi motivi.
diff --git a/src/HW/logscale-calc-tools/du2html.xsl b/src/HW/logscale-calc-tools/du2html.xsl
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+../../../templates/du2html.xsl \ No newline at end of file
diff --git a/src/tags/vintage/document-listing.tt b/src/tags/vintage/document-listing.tt
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+../../../templates/document-listing.tt \ No newline at end of file
diff --git a/src/tags/vintage/document.en.rest.tt b/src/tags/vintage/document.en.rest.tt
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@@ -0,0 +1,7 @@
+=======
+vintage
+=======
+:CreationDate: 2011-05-23 18:46:11
+:feed:
+
+[% PROCESS 'document-listing.tt' %]
diff --git a/src/tags/vintage/document.it.rest.tt b/src/tags/vintage/document.it.rest.tt
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+=======
+vintage
+=======
+:CreationDate: 2011-05-23 18:46:11
+:feed:
+
+[% PROCESS 'document-listing.tt' %]
diff --git a/src/tags/vintage/du2html.xsl b/src/tags/vintage/du2html.xsl
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+../../../templates/du2html.xsl \ No newline at end of file