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Kalid’s “Gentle introduction to calculus”

Kalid’s “Gentle introduction to calculus”. Using the circle. Take any circle:. Draw as many rings inside the circle as you can:. “Unroll” the rings and line them up like this:. If you split the circle into more rings. If you split the circle into more rings...they’d be skinnier than these.

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Kalid’s “Gentle introduction to calculus”

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  1. Kalid’s “Gentle introduction to calculus” Using the circle Concept by Kalid Azad Slide Show by Audrey McGoldrick

  2. Take any circle: Concept by Kalid Azad Slide Show by Audrey McGoldrick

  3. Draw as many rings inside the circle as you can: “Unroll” the rings and line them up like this: Concept by Kalid Azad Slide Show by Audrey McGoldrick

  4. If you split the circle into more rings... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  5. If you split the circle into more rings...they’d be skinnier than these... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  6. If you split the circle into more rings...they’d be skinnier than these... ...and this would become... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  7. If you split the circle into more rings...they’d be skinnier than these... ...and this would become... ...this!... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  8. If you split the circle into more rings...they’d be skinnier than these... ...and this would become... ...this!... ...which is even prettier, and closer to a right triangle! Concept by Kalid Azad Slide Show by Audrey McGoldrick

  9. If you do this long enough, eventually you will have... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  10. If you do this long enough, eventually you will have... ...this triangle... Concept by Kalid Azad Slide Show by Audrey McGoldrick

  11. ...whose area must equal the area of the original circle! Concept by Kalid Azad Slide Show by Audrey McGoldrick

  12. This side must be the radius of the circle Concept by Kalid Azad Slide Show by Audrey McGoldrick

  13. r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  14. ..and this side must be... r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  15. ..and this side must be... ..its circumference! r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  16. r 2r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  17. Use that good old formula for area of a triangle.... r 2r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  18. Use that good old formula for area of a triangle... r·2r r 2r 2r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  19. Use that good old formula for area of a triangle...and with a bit of algebra: r2 r·2r r 2r r Concept by Kalid Azad Slide Show by Audrey McGoldrick

  20. And voila! Concept by Kalid Azad Slide Show by Audrey McGoldrick

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