Demonstrating the notion of Proportion in Mixtures
with combinations of juices

Coffee, V-8 Smoothie, Carrot juice, V-8, Tomato juice, Half-and-half, Lime juice, water

Discussing sequences and series
with laptops and Maple software

> limit((4*n^2+5*n+2)^(1/2)-2*n,n=infinity);

> subs(n=10000,(4*n^2+5*n+2)^(1/2)-2*n);

> evalf(%);

>

recalling the trigonometric series expression,
demonstrating wave motion
with masses on springs

Motion detector records position data, computer gives Fourier transform
by plotting the amplitudes --- the coefficients A_n=(a_n²+b_n²)^(1/2) --- for a range of frequencies f₁...f_N.

Making remarks after Adam Coffman's discussion of the continuous Fourier transform