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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 `_ o `Eric Marcotte's one +`_. + +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 `_ 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 new file mode 100644 index 0000000..109ff63 --- /dev/null +++ b/src/HW/logscale-calc-tools/document.it.rest.txt @@ -0,0 +1,139 @@ +============================================= +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 +`_ o `quello di Eric Marcotte +`_. + +Va be', facciamo finta di aver capito… +====================================== + +Ho sotto mano un regolo "classico", e un regolo cilindrico (tipo `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 new file mode 120000 index 0000000..e2487e0 --- /dev/null +++ b/src/HW/logscale-calc-tools/du2html.xsl @@ -0,0 +1 @@ +../../../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 new file mode 120000 index 0000000..88c3968 --- /dev/null +++ b/src/tags/vintage/document-listing.tt @@ -0,0 +1 @@ +../../../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 new file mode 100644 index 0000000..5038648 --- /dev/null +++ b/src/tags/vintage/document.en.rest.tt @@ -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 new file mode 100644 index 0000000..5038648 --- /dev/null +++ b/src/tags/vintage/document.it.rest.tt @@ -0,0 +1,7 @@ +======= +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 new file mode 120000 index 0000000..e2487e0 --- /dev/null +++ b/src/tags/vintage/du2html.xsl @@ -0,0 +1 @@ +../../../templates/du2html.xsl \ No newline at end of file -- cgit v1.2.3