visual mathematics - ``i see dead easy proofs'' · visual mathematics \i see dead easy...
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Visual Mathematics“I See Dead Easy Proofs”
Joe Hurd@gilith
Ignite Portland 923 September 2010
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Mathematics is no more about formulas thanastronomy is about telescopes
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↙
↖let fc(z) = z2 + c in{z∣∣∣ lim
n→∞f nz (0) 6→ ∞
}
←−
←−
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Warm-up puzzle
+ 32 x →
+ 31 x → ?
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32 x
30 x
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32 x 32 x25 x 24 x
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Geometry
![Page 8: Visual Mathematics - ``I See Dead Easy Proofs'' · Visual Mathematics \I See Dead Easy Proofs" Joe Hurd ... Mathematics is no more about formulas than astronomy is about telescopes.-let](https://reader031.vdocuments.mx/reader031/viewer/2022020204/5b6087f67f8b9a36488b5f0e/html5/thumbnails/8.jpg)
?
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Number Theory
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1 = 1 = 1 × 11 + 3 = 4 = 2 × 21 + 3 + 5 = 9 = 3 × 31 + 3 + 5 + 7 = 16 = 4 × 41 + 3 + 5 + 7 + 9 = 25 = 5 × 5. . .
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1 + 2 + 3 + · · · + n = ?
n
n
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1 + 2 + 3 + · · · + n = 12 × n × (n + 1)
n
n + 1
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Pythagoras’ Theorem
a + b = c2 2 2
a
b
c
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blue area=
red area
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For this proof you will need:
b
b
a
a
1 x (a + b)-sided square 4 x right-angled triangle
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Assemble the proof (twice):
b
b
a
a b
b
a
a
Left over space= blue area
Left over space= red area
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Assemble the proof (twice):
b
b
a
a b
b
a
a
Left over space= blue area
Left over space= red area
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Thank you for your attention