How to Create Higher Exponential Powers Geometrically
Look at these similar triangles, and therefore the proportion {DG}/{DH}={DE}/{DF}., Make horizontal line DH of length 1, extend DF by length x from DH and raise DG of length y at an angle above horizontal DF., Create exponential powers by merely...
Step-by-Step Guide
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Step 1: Look at these similar triangles
You can use it to perform multiplication and division.
Open a new workbook in Excel and copy the drawing to experiment with it. , Draw HG and construct a line through F parallel to HG.
Let it intersect DG at E., Then DE will have length x^2., For example, to obtain x^3, use the relation DE/DH = DC/DF which becomes DE/1 = DC/DF, which becomes DE*DF = DC, and since DE = x^2 and DF = x, then DC = x^3.
See Diagram below.
This works because the lines EH and CF are parallel and so the triangles are similar and Euclid's theorem holds.,, Use relation DC/DH = DB/DF; DC/1 = DB/DF; DC*DF = DB; thus x^3 * x = x^4., For more art charts and graphs, you might also want to click on Category:
Microsoft Excel Imagery, Category:
Mathematics, Category:
Spreadsheets or Category:
Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page. -
Step 2: and therefore the proportion {DG}/{DH}={DE}/{DF}.
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Step 3: Make horizontal line DH of length 1
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Step 4: extend DF by length x from DH and raise DG of length y at an angle above horizontal DF.
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Step 5: Create exponential powers by merely making DG of length y from horizontal DF equal to DF of length x from DH.
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Step 6: Repeat the process for x^3
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Step 7: using the new y length each time.
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Step 8: Obtain x^4 by connecting HC and drawing the parallel to HC up from F to point B extended on ray DC to create line FB.
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Step 9: Make use of helper articles when proceeding through this tutorial: See the article How to Create a Spirallic Spin Particle Path or Necklace Form or Spherical Border for a list of articles related to Excel
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Step 10: Geometric and/or Trigonometric Art
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Step 11: Charting/Diagramming and Algebraic Formulation.
Detailed Guide
You can use it to perform multiplication and division.
Open a new workbook in Excel and copy the drawing to experiment with it. , Draw HG and construct a line through F parallel to HG.
Let it intersect DG at E., Then DE will have length x^2., For example, to obtain x^3, use the relation DE/DH = DC/DF which becomes DE/1 = DC/DF, which becomes DE*DF = DC, and since DE = x^2 and DF = x, then DC = x^3.
See Diagram below.
This works because the lines EH and CF are parallel and so the triangles are similar and Euclid's theorem holds.,, Use relation DC/DH = DB/DF; DC/1 = DB/DF; DC*DF = DB; thus x^3 * x = x^4., For more art charts and graphs, you might also want to click on Category:
Microsoft Excel Imagery, Category:
Mathematics, Category:
Spreadsheets or Category:
Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.
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Paul Morris
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