206^2 = 42436 and 208^2 = 43264
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Wednesday, May 4, 2011
Squares and cubes of 2 numbers using the same digits:
102^2 = 10404 and 201^2 = 40401
102^3 = 1,061,208 and 201^3 = 8,120,601.
Digits
202^3 = 8,242,408 = (–8 + 242 – 40 + 8)^3
204 = 3^2 + 7^2 + 5^2 + 11^2 = 2^2 + 8^2 + 6^2 + 10^2,
where 3+7 = 2+8 and after adding 3 to each digit: 6+10 = 5+11.
204^2 = 23^3 + 24^3 + 25^3 = 41,616.
206^3 = 8,741,816 = (8 + 7 + 4 + 181 + 6)^3
208^3 = 8,998,912 = (08 + 99 + 89 + 12)^3
209 = 1^6 + 2^5 + 3^4 + 4^3 + 5^2 + 6^1
305^3 = 28,372,625 = (283 + 7 + 2 + 6 + 2 + 5)^3
494 + 209 = 703 and 494,209 = 703^2
88+209 = 297 and 88,209 = 297^2 and 494+209 = 703 and 494,209 = 703^2 and 297+703 = 1000
2,401 = (2 + 4 + 0 + 1)^4 = 7^4
10,000 = (1+2+3+4)^4 = [(1^5+2^5+3^5+4^5)+(1^7+2^7+3^7+4^7)]/2
Reversible numbers and their squares:
102^2 = 10404 and 201^2 = 40401.
103^2 = 10609 and 301^2 = 90601.
Square numbers using the same digits:
108^2 = 11664, 129^2 = 16641 and 204^2 = 41616
148^2 = 21904, 203^2 = 41209 and 302^2 = 91204.
102^2 = 10404 ... 120^2 = 14400 ... 201^2 = 40401 ... 210^2 = 44100.
148^2 = 21904 ... 203^2 = 41209 ... 302^2 = 91204.
130^2 = 16900 ... 140^2 = 19600 ... 310^2 = 96100,
103^2 = 10609 ... 247^2 = 61009 ... 301^2 = 90601.
207^2 = 42849, 222^2 = 49284 and 288^2 = 82944
128^2 = 16,384, 178^2 = 31,684, 191^2 = 36,481, 196^2 = 38,416 and 209^2 = 43,681.
Monday, May 2, 2011
tan(4*pi/3) and arctan(4*pi/3)
tan(4*pi/3)
tan(4*pi/3) is clearly an irrational number. How to that arctan(4*pi/3), in radians, is irrational?
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