Math games Mathematical games in the history of mathematics
Beautiful Minds • The Franciscan Luca Pacioli (1445-1514) it is a primary figure of the mathematics of the XV-XVI century. • Pacioli remembers the introduction of the "double match"… • ... and for many games mathematicians that today they inspire our races!
Quadrati magici e giochi matematici Magic squares and mathematical games • The famous Propositiones ad acuendos juvenes of Alcuino of York (735-804) are the first collection of mathematician problems in Latin • Even the great philosopher John Locke (1632-1704) ... • ... not to mention Goethe that in Faust ...
I “quadrati magici”…partendo dalla Cina, VI sec. a.C The "magic squares" ... starting from China, 6th century a.C. • The oldest magic square is the Chinese Lo Shu, the only magic square classic of order 3 (a part of the symmetric...) • Interest in these "Games" spread in West with Melancholy by A. Dürer (1514). • B. Frenicle de Bessy (1605-1675) found 880 magic squares of order 4.
Quadrati magici nel XIV secolo Magic squares in the fourteenth century • The introduction of the magic squares in Europe was attributed to • M. Moschopulos around 1415-1420, • but there they are previous manuscripts (the squares of the Bolognese one of 1339 are in Pacioli). • Some of the squares (from 3 × 3 to 9 × 9) of Pacioli find themselves in the De occulta philosophia tres books by Cornelio Agrippa (Anversa, 1531).
I quadrati magici oggi The magic squares today • The mathematics from Frenicle has achieved many results about the magic squares. Important is ... • ... the order of the square to be built: it can be odd (like for the Lo Shu square, n = 3) or even (as per that of Dürer: n = 4).
The magic squares today • We start to pose 1 in the box in the middle of the first line. • Then we place the other numbers, in order, according to one "diagonal ascending", respecting some rules.
1
The magic squares today • Rules for "Diagonal": • go to the column next in case end of column; • go to the line previous in case end of line; • go to the box lower
17
24
1
8
15
23
5
7
14
16
4
6
13
20
22
10
12
19
21
3
11
18
25
2
9
And finally ... let's check! • We find the constant magic: sum • of numbers from 1 to 25: 25 × 26: 2 = 325 • 325: 5 = 65
65 65 5 65 65
17
24
1
8
15
23
5
7
14
16
4
6
13
20
22
10
12
19
21
3
11
18
25
2
9
65
65
65
65
65 65 65 65
Thank you all for your attention • The Italian team
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magic square with key 15