A gift from friends several years ago, it used to hang in my campus office. Interestingly, though there would be many, many possibilities, *π* does not figure in any of these expressions for the numbers 1–12! (E.g., cos(*π*/2) = 1 so 2 = *π*/arccos(1).) Nevertheless, it's appropriate for Pi Day because the clock is a *circle*. :-)

1 using the exact value of Legendre’s constant

2 as a geometric series (with ½)

3 encoded for html (HyperText Markup Language)

4 is the modular inverse of 2 (mod 7) because 2 × 4 = 8 = 1 (mod 7).

5 expressed in terms of the so-called “Golden ratio”

6 = 3 factorial = 3! = 3 × 2 × 1 = 6

7 A nice exercise in theorem-proving!*

8 as a binary number (right-to-left: 0 units, 0 first-powers, 0 squares, 1 cube)

9 as base 4 (“quaternary”) representation: 21 = 2 × 4¹ + 1 × 4⁰

10 is the number of “combinations” picking 2 things*unordered* from 5 things

11 in hexidecimal representation (0x indicates hexidecimal and 0B is 11)

12³ = 1728, so the cube root of 1728 is 12

~~~~~~~~~~~~~~~~

***Proof** that 6.9999… = 7:

(a) 6.99999… = 7

Multiply both sides by 10:

(b) 69.9999… = 70

Subtract (a) from (b):

69.9999… – 6.9999… = 70 – 7 ==> 63 = 63.*QED*

*Looking back*

1 year ago: “Inside a fitness machine”

2 years ago:*No post*

3 years ago: “Something circular”

4 years ago: “Pi Day, 2017”

5 years ago: “Pi Day, 2016”

6 years ago: “Something round for Pi Day”

7 years ago: “Pi Day, 2014”

8 years ago: “Pi Day”

9 years ago: “Pi in the Rocks?”

10 years ago: “Am I a bit ‘left-of-center’?”

[ PXL_20210315_021828773e280cwS7x7Atm :: cell phone ]

1 using the exact value of Legendre’s constant

2 as a geometric series (with ½)

3 encoded for html (HyperText Markup Language)

4 is the modular inverse of 2 (mod 7) because 2 × 4 = 8 = 1 (mod 7).

5 expressed in terms of the so-called “Golden ratio”

6 = 3 factorial = 3! = 3 × 2 × 1 = 6

7 A nice exercise in theorem-proving!*

8 as a binary number (right-to-left: 0 units, 0 first-powers, 0 squares, 1 cube)

9 as base 4 (“quaternary”) representation: 21 = 2 × 4¹ + 1 × 4⁰

10 is the number of “combinations” picking 2 things

11 in hexidecimal representation (0x indicates hexidecimal and 0B is 11)

12³ = 1728, so the cube root of 1728 is 12

~~~~~~~~~~~~~~~~

*

(a) 6.99999… = 7

Multiply both sides by 10:

(b) 69.9999… = 70

Subtract (a) from (b):

69.9999… – 6.9999… = 70 – 7 ==> 63 = 63.

1 year ago: “Inside a fitness machine”

2 years ago:

3 years ago: “Something circular”

4 years ago: “Pi Day, 2017”

5 years ago: “Pi Day, 2016”

6 years ago: “Something round for Pi Day”

7 years ago: “Pi Day, 2014”

8 years ago: “Pi Day”

9 years ago: “Pi in the Rocks?”

10 years ago: “Am I a bit ‘left-of-center’?”

[ PXL_20210315_021828773e280cwS7x7Atm :: cell phone ]

marlboromaam (Mags)
ace

Wow! What a cool clock.

May 10th, 2021

Thom Mitchell

@dutchothotmailcom Thinking of your son…

May 10th, 2021

PhotoCrazy
ace

Cool clock!

May 10th, 2021

GaryW

Neat clock!

May 11th, 2021

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