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Riemann Zeta Curve

Riemann Zeta Curve 3d printed Polished steel Zetaness
Polished steel Zetaness
Riemann Zeta Curve 3d printed Polished steel Zetaness
Riemann Zeta Curve 3d printed Polished steel Zetaness
Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed In Pink Strong and Flexible, as an earring.
Riemann Zeta Curve 3d printed In Pink Strong and Flexible, as an earring.
Riemann Zeta Curve 3d printed Pink Strong and Flexible, as an earring.
Riemann Zeta Curve 3d printed Pink Strong and Flexible, as an earring.
Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
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Riemann Zeta Curve 3d printed
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Products
First to try

Plastic

  • White Strong & Flexible Polished

    White nylon plastic polished to reveal a smooth matte finish.

    5.000000
  • Polished Metallic Plastic

    Grey nylon plastic with a subtle metallic sparkle and polished sheen (formerly Polished Alumide.)

    4.750000
  • Blue Strong & Flexible Polished

    Dark blue, richly colored nylon plastic with a smooth finish.

    5.500000
  • Purple Strong & Flexible Polished

    Dark purple, richly colored nylon plastic with a smooth finish.

    5.500000
  • Red Strong & Flexible Polished

    Pinkish red, richly colored nylon plastic with a smooth finish.

    5.500000
  • Pink Strong & Flexible Polished

    Bright pink, richly colored nylon plastic with a smooth finish.

    5.500000
  • Yellow Strong & Flexible Polished

    Deep yellow, richly colored nylon plastic with a smooth finish.

    5.500000
  • Green Strong & Flexible Polished

    Deep green, richly colored nylon plastic with a smooth finish.

    5.500000
  • Orange Strong & Flexible Polished

    Bright orange, richly colored nylon plastic with a smooth finish.

    5.500000
  • White Strong & Flexible

    White nylon plastic with a matte finish and slight grainy feel.

    4.500000
  • Black Strong & Flexible

    Black nylon plastic with a matte finish and slight grainy feel.

    5.000000
  • Metallic Plastic

    Grey nylon plastic with a subtle metallic sparkle (formerly Alumide.)

    4.750000
  • White Acrylic

    Firm white plastic with a smooth surface and rubbery feel.

    6.750000
  • Black Acrylic

    Firm black plastic with a smooth surface and rubbery feel.

    6.750000
  • Transparent Acrylic

    Firm translucent plastic with a smooth surface and rubbery feel.

    6.750000
  • Frosted Ultra Detail

    Matte translucent plastic that showcases fine and intricate details.

    10.000000
  • White Strong & Flexible

    White nylon plastic with a matte finish and slight grainy feel.

    $4.50

About this Product

This is a parametric graph of the Reimann Zeta Function, on the critical line ℜ(z)=1/2, in the region 0 ≤ ℑ(z) ≤ 50 (units are millimeters). To be precise, the equations of the curve in parameter t are:

x = t
y = 3×ℜ(ζ(½ + ti))
z = 3×ℑ(ζ(½ + ti))

The straight line represents the critical line, and the displacements from the axis at each point are the real and imaginary parts of the function ζ(z), multiplied by three, because otherwise it just looks too skinny. Visible are ten non-trivial roots of the zeta function, at approximately the following values of ℑ(z):

14.13425
21.02204
25.01086
30.42488
32.93506
37.58618
40.91872
43.32707
48.00515
49.77383

Makes for a unique pendant, or earrings, if your neck is long enough (note: price is for one unit; if you want earrings, you need to order two, and supply your own earring hooks.)

What's in the Box
INCM

Riemann Zeta Curve in White Strong & Flexible
Width Height Depth
6.084 cm 1.724 cm 1.55 cm
This model is 3D Printed in White Strong & Flexible: White nylon plastic with a matte finish and slight grainy feel.
Model version 5 | Last updated on 09/16/2014

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Products
First to try

Plastic

  • White Strong & Flexible Polished

    White nylon plastic polished to reveal a smooth matte finish.

    5.000000
  • Polished Metallic Plastic

    Grey nylon plastic with a subtle metallic sparkle and polished sheen (formerly Polished Alumide.)

    4.750000
  • Blue Strong & Flexible Polished

    Dark blue, richly colored nylon plastic with a smooth finish.

    5.500000
  • Purple Strong & Flexible Polished

    Dark purple, richly colored nylon plastic with a smooth finish.

    5.500000
  • Red Strong & Flexible Polished

    Pinkish red, richly colored nylon plastic with a smooth finish.

    5.500000
  • Pink Strong & Flexible Polished

    Bright pink, richly colored nylon plastic with a smooth finish.

    5.500000
  • Yellow Strong & Flexible Polished

    Deep yellow, richly colored nylon plastic with a smooth finish.

    5.500000
  • Green Strong & Flexible Polished

    Deep green, richly colored nylon plastic with a smooth finish.

    5.500000
  • Orange Strong & Flexible Polished

    Bright orange, richly colored nylon plastic with a smooth finish.

    5.500000
  • White Strong & Flexible

    White nylon plastic with a matte finish and slight grainy feel.

    4.500000
  • Black Strong & Flexible

    Black nylon plastic with a matte finish and slight grainy feel.

    5.000000
  • Metallic Plastic

    Grey nylon plastic with a subtle metallic sparkle (formerly Alumide.)

    4.750000
  • White Acrylic

    Firm white plastic with a smooth surface and rubbery feel.

    6.750000
  • Black Acrylic

    Firm black plastic with a smooth surface and rubbery feel.

    6.750000
  • Transparent Acrylic

    Firm translucent plastic with a smooth surface and rubbery feel.

    6.750000
  • Frosted Ultra Detail

    Matte translucent plastic that showcases fine and intricate details.

    10.000000
  • White Strong & Flexible

    White nylon plastic with a matte finish and slight grainy feel.

    $4.50

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