...sides of a triangle, expand yy = (ß— a)«(/3 — a) to obtain the law of cosines. 10. Show that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides. What does the difference of the squares of the diagonals equal ? 11. Show that — — a...

...projection of 6 on c from a positive sect through zero on to increasingly large negative sects. 2. The sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the four sides. 3. The sum of the squares of the diagonals of a quadrilateral equals the sum of the...

...angle of the triangle whose sides are 12, 35, and 37 acute, right, or obtuse ? Ex. 142. Prove that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides of the parallelogram. (Use § 310 and § 311.) Ex. 143. If AB and AC are the equal sides...

...I!, remarked "I don't know how to do that". The class had a problem involving the proposition nrnhe sum of the squares of the diagonals of a parallelogram, equals the sum of the squares of the four sides". The instructor said : "From this we get 2 AB2+ 2 BC2= AC"2* ID2. M. immediately remarked...

...angle of the triangle whose sides are 12, 35, and 37 acute, right, or obtuse ? Ex. 142. Prove that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides of the parallelogram. (Use § 310 and § 311.) Ex. 143. If AB and AC are the equal sides...

...the parallelogram law for L2: Is this true for Lp when p ^ 2 ? The geometric interpretation is that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides. 19. Prove that a finite dimensional Hilbert space is isometric with R" for some n. 20. Construct...

...product to prove the following theorems of elementary geometry: a) The cosine law for a triangle; b) The sum of the squares of the diagonals of a parallelogram equals twice the sum of the squares of two adjacent sides of the parallelogram; c) The diagonals of a rhombus...

...-\\XY\\* (b) ||A- + y||2 + HA" - yf = 2||A||2 + 2||yf . Show with a picture how this formula states that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides. 15. For each part find the projection of Y onto A — S-'rZ and the distance from y to A....

...be a closed subspace — that is, a Hilbert subspace — of H. The Parallelogram Law: Ifx, ye H then (the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the four sides — see Figure 1). Figure 1. The parallelogram law. If KCH is a closed subspace, then...

...prove that This identity already contains an important law of Euclidean geometry; it tells us that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides. HILBERT SPACE PROJECTION THEOREM. If H0 is a closed linear subspace of the Hilbert space...