Pasta e Fagioli Soup

INGREDIENTS

  • 2 cups ditalini pasta
  • 2 tablespoons olive oil
  • 1 pound ground spicy Italian sausage
  • 1 small yellow onion diced
  • 1 tablespoon minced garlic
  • 3 carrots peeled and diced
  • 1 stalk celery diced
  • 1 14.5 ounce can diced tomatoes
  • 2 tablespoons tomato paste
  • 1 teaspoon dried basil
  • 1 teaspoon dried Italian seasoning
  • 1 teaspoon dried thyme
  • 1 teaspoon dried rosemary
  • 1 teaspoon red pepper flakes
  • 1 15 ounce can tomato sauce no salt added
  • 6 cups low sodium chicken broth
  • 1 15 ounce can red kidney beans drained and rinsed
  • 1 15 ounce can Great Northern beans drained and rinsed
  • Kosher salt and freshly ground black pepper to taste

INSTRUCTIONS

  1. Place a large soup pot or Dutch oven over medium heat and add olive olive oil. Once the oil is hot, add ground Italian sausage and cook without moving for about one minute. Crumble it using a wooden spoon and continue cooking until browned, about 3-5 minutes. If needed, drain excess fat.

  2. Push cooked sausage to one side of the pot, so it covers only half of the bottom of the pot or Dutch oven. Add onion and garlic to the other half and cook for 1-2 minutes, stirring occasionally, until the onion is tender.

  3. Stir to combine the browned sausage with the onion and garlic.

  4. Add chopped carrots, celery, diced tomatoes and tomato paste. Stir and cook until tender, for about 4-5 minutes, stirring occasionally.

  5. Add dried basil, dried Italian seasoning, dried thyme, dried rosemary and red pepper flakes. Stir to combine.

  6. Add tomato sauce, chicken broth and drained and rinsed beans. Season with salt and pepper, to taste.

  7. Bring to a boil, reduce heat to low and simmer, covered for about 10-15 minutes or until vegetables are tender. If needed, add more water, one cup at a time.

  8. In the meantime, add water a large pot over medium-high heat, season with salt. Bring to a boil and cook pasta according to package instructions. Drain well, toss with a bit of olive oil and set aside.

  9. Once vegetables are tender, stir in pasta until heated through.

  10. Garnish with parsley if desired, and serve immediately.

Dandelin spheres -Conic Sections Proof of Circle Ellipse Parabola Hyperbola

Research Links

 

Ellipse Proof: The sum of distances d(F1P) + d(F2P) remain constant as the point P moves along the curve.

  • A line passing through P and the vertex S of the cone intersects the two circles at points P1 and P2.
  • As P moves along the curve, P1 and P2 move along the two circles.
  • The distance from F1 to P is the same as the distance from P1 to P, because these distances are the lengths of the line segments PF1 and PP1, which have a common endpoint P and are both tangent to the same sphere (G1) at their other endpoints.
  • Likewise, by a symmetrical argument, the distance from F2 to P is the same as the distance from P2 to P.
  • Consequently, the sum of distances d(F1P) + d(F2P) must be constant as P moves along the curve because the sum of distances d(P1P) + d(P2P) also remains constant. Therefore, the curve is an ellipse.  This follows from the fact that P lies on the straight line from P1 to P2, and the distance from P1 to P2 remains constant.

Ohio Old Wooden House Siding Solutions

Metal Siding Research Links

Wood Siding 

Following video shows an open Brazilian ipe wood solution where the house is house wrapped with Cosella Dorken Delta – Fassade S and covered with boards that are spaced so the wrap does all the water sealing.  Open joint cladding requires extreme UV resistance.  Delta – Fassade S is quoted as being designed specifically for open joint cladding.