Long Division Style
The Quadratic Formula Song
Music versions of math formulas and procedures are not new. One that came up recently in the Algebra class I teach for in-service teachers is the Quadratic Formula, set to the tune Pop Goes the Weasel.
x equals negative b
plus or minus the square root
of b squared minus 4ac
all over 2a
Please sing this to your students!
Solving the Cubic in a Poem
Did you know that there is something similar for the Cubic Formula? Tartaglia was one of the first mathematicians to solve (a specific form of) the cubic. His solution was secret, but he did communicate his solution to Cardano in a poem, but swore Cardano to secrecy.
Here’s the poem, in translation (from the MAA Digital Library, a fantastic resource).
Tartaglia divulged to Hieronimo Cardano (1501-1576) the solution of the three cubic equations without the quadratic term on March 25, 1539 in Cardano’s house in Milano in the form of a famous poem (translated here by the author):
01) When the cube with the cose beside it
02) Equates itself to some other whole number, <=q>
03) Find two other, of which it is the difference.
04) Hereafter you will consider this customarily
05) That their product always will be equal
06) To the third of the cube of the cose net. 3/3, instead of (p/3)3>
07) Its general remainder then
08) Of their cube sides , well subtracted,
09) Will be the value of your principal unknown. <=x>
10) In the second of these acts,
11) When the cube remains solo ,
12) You will observe these other arrangements:
13) Of the numberyou will quickly make two such parts,
14) That the one times the other will produce straightforward
15) The third of the cube of the cose in a multitude,
16) Of which then, per common precept,
17) You will take the cube sides joined together.
19) The third then of these our calculations
20) Solves itself with the second, if you look well after,
21) That by nature they are quasi conjoined.
22) I found these, & not with slow steps,
23) In thousand five hundred, four and thirty
24) With very firm and strong foundations
25) In the city girded around by the sea.