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Geometric Analysis of Suction Feeding

Geometric Analysis of Suction Feeding. Math & Nature. The universe is written in the language of mathematics Galileo Galilei , 1623 Quantitative analysis of natural phenomena is at the heart of scientific inquiry Nature provides a tangible context for mathematics instruction .

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Geometric Analysis of Suction Feeding

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  1. Geometric Analysis of Suction Feeding

  2. Math & Nature • The universe is written in the language of mathematics • Galileo Galilei, 1623 • Quantitative analysis of natural phenomena is at the heart of scientific inquiry • Nature provides a tangible context for mathematics instruction

  3. The Importance of Context • Context • The part of a text or statement that surrounds a particular word or passage and determines its meaning. • The circumstances in which an event occurs; a setting.

  4. The Importance of Context • Context-Specific Learning • Facilitates experiential and associative learning • Demonstration, activation, application, task-centered, and integration principles (Merrill 2002) • Facilitates generalization of principles to other contexts

  5. Math & Nature • Geometry & Biology • Biological structures vary greatly in geometry and therefore represent a platform for geometric education • Geometric variability  functional variability  ecological variability • Mechanism for illustrating the consequences of geometry

  6. Math & Nature • Vertebrate skulls vary greatly in form & function  www.digimorph.org

  7. Math & Nature • Vertebrate skulls vary greatly in form & function ~50 bones ~7 moving parts 22 bones 1 moving part  www.digimorph.org  csi.whoi.edu

  8. Math & Nature • Vertebrate skulls vary greatly in form & function Liem et al. (2001)

  9. Math & Nature • Vertebrate skulls vary greatly in form & function • Moveable parts of the fish skull are responsible for the diversity of feeding mechanisms in fish • Jaw protrusion in the sand tiger shark Carcharias taurus  D. Huber

  10. Math & Nature • Vertebrate skulls vary greatly in form & function • Moveable parts of the fish skull are responsible for the diversity of feeding mechanisms in fish • Jaw protrusion in the sling-jaw wrasse Epibulusinsidiator  P. Wainwright

  11. Math & Nature • Fish feeding mechanisms • Filter • Biting • Ram • Suction  www.true-wildlife.blogspot.com  www.z00n.net  C. Fallows

  12. Math & Nature • Fish feeding mechanisms • Filter feeding  W. Mischler 2013 Motta et al. (2010)

  13. Math & Nature • Fish feeding mechanisms • Filter feeding Motta et al. (2010)

  14. Math & Nature • Fish feeding mechanisms • Filter feeding  P. Motta

  15. Math & Nature • Fish feeding mechanisms • Biting

  16. Math & Nature • Fish feeding mechanisms • Biting  www.digimorph.org

  17. Math & Nature • Fish feeding mechanisms • Ram feeding  D. Huber  C. Fallows

  18. Math & Nature • Fish feeding mechanisms • Ram feeding  S. Huskey  www.tennesseeaquarium.com

  19. Math & Nature • Fish feeding mechanisms • Ram feeding  D. Huber

  20. Math & Nature • Fish feeding mechanisms • Suction feeding • Most common fish feeding mechanism • Water cohesion • Suction performance  D. Huber

  21. Math & Nature • Fish feeding mechanisms • Suction feeding • http://www.youtube.com/user/Wainwrightlab Wainwright et al (2006)

  22. Math & Nature • Fish feeding mechanisms • Suction feeding • http://www.youtube.com/user/Wainwrightlab Svanback et al (2002)

  23. Math & Nature • Fish feeding mechanisms • Suction feeding • http://www.youtube.com/user/Wainwrightlab Grubich (2001)

  24. Math & Nature • Fish feeding mechanisms • Suction feeding • Anterior  posterior expansion Gibb & Ferry-Graham (2005) Wainwright et al (2006)

  25. Math & Nature • Fish feeding mechanisms • Suction feeding • Fluid flow Holzmanet al (2008)

  26. Math & Nature • Fish feeding mechanisms • Suction feeding • Fluid pressure and movement speed Svanback et al (2002)

  27. Math & Nature • Fish feeding mechanisms • Suction feeding • Feeding ecology Motta et al (2008)

  28. Math & Nature • Fish feeding mechanisms • Suction feeding • Geometric modeling Van Wassenbergh et al (2007) Bishop et al (2008)

  29. Math & Nature • Fish feeding mechanisms • Suction feeding • Goliath grouper Epinephelusitajara

  30. Math & Nature • Fish feeding mechanisms • Suction feeding • Goliath grouper Epinephelusitajara • Questions • What fluid velocity can the goliath grouper generate during suction feeding? • How does suction feeding by the goliath grouper compare to other fish?

  31. Math & Nature • Geometry & Biology • NGSSS • MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and area. • MA.912.G.5.4: Solve real-world problems involving right triangles. • MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.

  32. Math & Nature • Geometry & Biology • NGSSS • MA.912.G.7.7: Determine how changes in dimension affect the surface area and volume of common geometric solids. • MA.912.G.8.2: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

  33. Math & Nature • Geometry & Biology • CCSS • MACC.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. • MACC.912.G-GMD.2.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

  34. Math & Nature • Geometry & Biology • CCSS • MACC.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). • MACC.K12.MP.1.1: Make sense of problems and persevere in solving them. • MACC.K12.MP.4.1: Model with mathematics

  35. Math & Nature • Goliath grouper model • Objective • Determine the velocity of water flow into the mouth • Procedure • Determine the volume of components A and B at rest (t0) and at maximum expansion (t1) • t0 = time at rest • t1 = time at maximum expansion • Determine the volume change during feeding A B A B

  36. Math & Nature • Goliath grouper model • Objective • Determine the velocity of water flow into the mouth • Procedure • Determine the area of the mouth at maximum expansion (t1) • t1 = time at maximum expansion A B A B

  37. Math & Nature • Goliath grouper model • Objective • Determine the velocity of water flow into the mouth • Procedure A B A B

  38. Math & Nature • Suction feeding in the goliath grouper • Given • Dimensions of cones A and B at rest (t0) • Find the volume of the goliath grouper feeding mechanism at rest (t0). b c e d a a

  39. Math & Nature • Suction feeding in the goliath grouper • Given • Dimensions of cones A and B at rest (t0) • Find the volume of the goliath grouper feeding mechanism at rest (t0). e c b d a a

  40. Math & Nature • Suction feeding in the goliath grouper • Given • Dimensions of cones A and B at maximum expansion (t1) • Find the volume of the goliath grouper feeding mechanism at maximum expansion (t1).

  41. Math & Nature • Suction feeding in the goliath grouper • Given • Dimensions of cone B at maximum expansion (t1) • Find the area of the goliath grouper mouth at maximum expansion (t1).  A. Collins mouth

  42. Math & Nature • Suction feeding in the goliath grouper • Given • Volume of the goliath grouper feeding mechanism at rest (t0) and at maximum expansion (t1) • Duration of the feeding event (t1 - t0) • Area of the mouth opening at maximum expansion (t1) • Find the velocity of water flow into the mouth of the goliath grouper during suction feeding.

  43. Math & Nature • Suction feeding in the snookCentropomusundecimalis  JJ Photo  Korhnak Wainwright et al (2006)

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