PlanetMath: Pythagorean hypotenuses as contraharmonic means

$c^2 \;=\; a^2+b^2$	$\displaystyle c \;=\; \frac{u^2+v^2}{u+v}$	Note
$5^2 = 3^2+4^2$	$5 = (2^2+6^2)/(2+6)$
$10^2 = 6^2+8^2$	$10 = (6^2+12^2)/(6+12)$
$13^2 = 5^2+12^2$	$13 = (3^2+15^2)/(3+15)$
$15^2 = 9^2+12^2$	$15 = (9^2+18^2)/(9+18)$
$17^2 = 8^2+15^2$	$17 = (5^2+20^2)/(5+20)$
$20^2 = 12^2+16^2$	$20 = (8^2+24^2)/(8+24)$
$25^2 = 7^2+24^2$	$25 = (4^2+28^2)/(4+28)$
$26^2 = 10^2+24^2$	$26 = (6^2+30^2)/(6+30)$
$29^2 = 20^2+21^2$	$29 = (14^2+35^2)/(14+35)$
$30^2 = 18^2+24^2$	$30 = (12^2+36^2)/(12+36)$
$34^2 = 16^2+30^2$	$34 = (10^2+40^2)/(10+40)$
$35^2 = 21^2+28^2$	$35 = (14^2+42^2)/(14+42)$
$37^2 = 12^2+35^2$	$37 = (30^2+42^2)/(30+42)$
$39^2 = 15^2+36^2$	$39 = (9^2+45^2)/(9+45)$
$40^2 = 24^2+32^2$	$40 = (16^2+48^2)/(16+48)$
$41^2 = 9^2+40^2$	$41 = (36^2+45^2)/(36+45)$
$50^2 = 14^2+48^2$	$50 = (42^2+56^2)/(42+56)$
$51^2 = 24^2+45^2$	$51 = (15^2+60^2)/(15+60)$
$52^2 = 20^2+48^2$	$52 = (12^2+60^2)/(12+60)$
$53^2 = 28^2+45^2$	$53 = (18^2+63^2)/(18+63)$
$55^2 = 33^2+44^2$	$55 = (22^2+66^2)/(22+66)$
$58^2 = 40^2+42^2$	$58 = (30^2+70^2)/(30+70)$
$60^2 = 36^2+48^2$	$60 = (24^2+72^2)/(24+72)$
$61^2 = 11^2+60^2$	$61 = (6^2+66^2)/(6+66)$
$65^2 = 39^2+52^2$	$65 = (26^2+78^2)/(26+78)$
$68^2 = 32^2+60^2$	$68 = (20^2+80^2)/(20+80)$
$70^2 = 42^2+56^2$	$70 = (28^2+84^2)/(28+84)$
$73^2 = 48^2+55^2$	$73 = (40^2+88^2)/(40+88)$
$74^2 = 24^2+70^2$	$74 = (14^2+84^2)/(14+84)$
$75^2 = 21^2+72^2$	$75 = (12^2+84^2)/(12+84)$
$78^2 = 30^2+72^2$	$78 = (18^2+90^2)/(18+90)$
$80^2 = 48^2+64^2$	$80 = (32^2+96^2)/(32+96)$
$82^2 = 18^2+80^2$	$82 = (10^2+90^2)/(10+90)$
$85^2 = 40^2+75^2$	$85 = (34^2+102^2)/(34+102)$
$87^2 = 60^2+63^2$	$87 = (42^2+105^2)/(42+105)$
$89^2 = 39^2+80^2$	$89 = (24^2+104^2)/(24+104)$
$90^2 = 54^2+72^2$	$90 = (36^2+108^2)/(36+108)$
$91^2 = 35^2+84^2$	$91 = (21^2+105^2)/(21+105)$
$95^2 = 57^2+76^2$	$95 = (38^2+114^2)/(38+114)$
$97^2 = 72^2+65^2$	$97 = (45^2+117^2)/(45+117)$
$100^2 = 60^2+80^2$	$100 = (40^2+120^2)/(40+120)$