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Size Matters: Area

Size Matters: Area. Toby Neal Sarabeth Royer Hannah Harris Megan Keller. What is “Area”!?. -put simply “area” is the size of a surface !. 1 block= 1 unit. Prevailing View Before Discovery of Formulas to Calculate Area . Method of Exhaustion: Sounds tedious! In order to determine the

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Size Matters: Area

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  1. Size Matters: Area Toby Neal Sarabeth Royer Hannah Harris Megan Keller

  2. What is “Area”!? -put simply “area” is the size of a surface! 1 block= 1 unit

  3. Prevailing View Before Discovery of Formulas to Calculate Area • Method of Exhaustion: • Sounds tedious! • In order to determine the area of a circle, mathematicians would inscribe polygons into circles, and continue adding more sides to polygons, becoming closer and closer to a circle to estimate the area. -This certainly looks exhausting

  4. History • They would then calculate the area of the triangles in the polygon to determine the area. • As the sides increased, they became closer and closer to discovering the actual area • Greek mathematician Archimedes (287 BC-212 BC) is said to have been the first to attempt this • Johannes Keppler tried even changing the circle into a distorted triangle to discover the area

  5. History • Any areas that were non-traditional and had either curves or odd shapes, were thus divided into smaller shapes where the area could be more easily calculated, and then added up • To a degree, this method is still used today • EX. Irregular Farm Fields

  6. 4 Step Process to Calculating the Area of a Field Step 1: Make a sketch of the field from a bird’s eye view and label the major corners

  7. Calculating the Area of a Field Step 2: Divide the field into shapes. Use the largest shapes possible and be sure to label the tips of the triangles. Step 3: Set out ranging poles and find the distance from AC and EC.

  8. Calculating the Area of a Field Step 4: Use the measurements of your field to calculate the area using a=1/2bh. Then add together all of the areas of the triangle.

  9. Why is this important?! • Knowing the area of a field can help to determine: • Nitrogen inputs • Fertilizer inputs • Phosphorous inputs • Seed planting ratios

  10. Example by Penn State Plant Science • You have a 50-lb bag of 26-5-10 fertilizer that you want to apply to a lawn at a rate of 1.0 lb nitrogen per 1000 sq ft. How much of the 26-5-10 fertilizer will you need to apply per 1000 sqft? • The quickest way to solve this problem is to ignore the weight of the fertilizer bag and simply divide the amount of nitrogen desired (1.0 lb nitrogen per 1000 sqft) by the percentage of nitrogen in the bag (26%). When using percentages in calculations, convert the number to its decimal form (for example, 26% = 0.26; 5% = 0.05). • (1.0 lb nitrogen per 1000 sqft) ÷ 0.26 = 3.8 lb of a 26-5-10 fertilizer is needed to supply 1.0 lb nitrogen per 1000 sq ft.

  11. The World Thanks Us! • By utilizing the proper calculations farmers everywhere can save money by not purchasing more material than they need. • Applying proper amounts of inputs relieves run-off of nutrient inputs that are damaging to the ecosystem.

  12. Sources • http://ec.europa.eu/agriculture/envir/report/en/nitro_en/report.htm • http://mathforum.org/library/drmath/view/55318.html • http://math.about.com/library/weekly/aa062502a.htm • http://en.wikipedia.org/wiki/History_of_calculus • http://plantscience.psu.edu/research/centers/turf/extension/factsheets/calculations-turfgrass-fertilization • http://www.fao.org/docrep/r7021e/r7021e06.htm

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