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  • londonskies commented on Epbot's instructable Penny Desk!7 months ago
    Penny Desk!

    I make it $2.96 per sq Ft.Calc:Hex-packed circle density is 0.90689968211 (all figures here are approx.)Diameter of US 1c = 19.05 mm. Area of 1c coin = pi*r^2 = pi*(19.05/2)^2 = 285.022956992 sqmm. Therefore close-packed 1c coins per sqm =1000*1000/285.022956992*0.90689968211 = 3181.84784721 or 3181.84784721/3.28084^2 per sq Ft = 295.603318905 1c coins per sq FtDom

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  • londonskies commented on Epbot's instructable Penny Desk!8 months ago
    Penny Desk!

    Great instructable thanks ... I didn't know about the blowtorch technique, useful to learn of this.To calculate how many coins you need you might want to adapt the following UK penny calculations to your preferred coin size ...How many British 1 pence coins could you fit in a meter squared?if 1p coin diameter= 20.3mm ...1p coins per sqm square packed: (1000/20.3)^2 = 2426.65. That s a coindensity of pi/4 or approx 78.54%.But lets work out the coin density if arranged in hexagonal closepacked layout, Let s work it out for circle of diameter=1 unit. Sketch4 adjacent circles with centres forming a rhombus. Within the rhombusyou have a pattern which when repeated describes the entire hexagonalclose-packed layout.Rhombus area = (1^2-.5^2)^.5 = .75^.5 = 0.86602540378Area which is within a cir...see more »Great instructable thanks ... I didn't know about the blowtorch technique, useful to learn of this.To calculate how many coins you need you might want to adapt the following UK penny calculations to your preferred coin size ...How many British 1 pence coins could you fit in a meter squared?if 1p coin diameter= 20.3mm ...1p coins per sqm square packed: (1000/20.3)^2 = 2426.65. That s a coindensity of pi/4 or approx 78.54%.But lets work out the coin density if arranged in hexagonal closepacked layout, Let s work it out for circle of diameter=1 unit. Sketch4 adjacent circles with centres forming a rhombus. Within the rhombusyou have a pattern which when repeated describes the entire hexagonalclose-packed layout.Rhombus area = (1^2-.5^2)^.5 = .75^.5 = 0.86602540378Area which is within a circle AND within rhombus =pi*.5^2 = 0.78539816339Therefore circle density is 0.78539816339/0.86602540378 =0.90689968211. A density of circa 90.69%.Area of 1p coin = pi*r^2 = pi*(20.3/2)^2 = 323.6547 sqmmTherefore close-packed coins per sqm =1000*1000/323.6547*0.90689968211 = 2802.05936175This doesn t account for edge conditions. circa 2802 coins per sqm. Good luck!Dominic P

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