Let a and b be positive numbers with a . b. Let a1 be their arithmetic mean and b1 their geometric mean: a1 a 1 b 2 b1 sab Repeat this process so that, in general, an11 an 1 bn 2 bn11 san bn (a) Use mathematical induction to show that an . an11 . bn11 . bn (b) Deduce that both han j and hbn j are convergent. (c) Show that limnl` an limnl` bn. Gauss called the common value of these limits the arithmetic-geometric mean of the numbers a and b
Module #18-‐ Basic concepts of sensation and perception Sunday, February 28, 2016 5:55 PM - Heather Sellersc 'urious mix of "perfect vision" and face blindness: the distinction between sensation and perception ○ Sensation: the process by which our sensory receptors and nervous system receive and represent stimulus energies from our environment (sensory receptors detect information→nervous system transmits the information to her brain) [normal] ○ Perception: the process of organizing and interpreting sensory information, enabling us to recognize meaningful objects and events [almost normal] ○ Bottom -‐up processing: analysis that begins with the sensory receptors and works up to the brain's integration of sensory information [build up from smallest pieces of sensory info/detect lines, angels, colors…] ○ Top-‐down processing: constructs perceptions from the sensory input by drawing on our experience and expectations [perception that's driven by perception/ the brain applies what y
