Weekly Photo Challenge: Converge

By Vladimir Brezina

A convergent infinite series

Convergent series

wherein the sum of an infinite number of alternating positive and negative terms, progressively decreasing in absolute magnitude, is the unity. (Borges would be pleased.)

Converging reflections 1
Converging reflections 2

A contribution to this week’s Photo Challenge, Converge.

45 responses to “Weekly Photo Challenge: Converge

  1. It is so creative to use math to show the concept of converge. I have been interested in math all my life, so I took a few minutes to verify the accuracy of the formula in your post.

    For alternative additions and subtractions, the left side of the formula can be simplified as (3/4 + 3/16 + 3/64 + …….). Then move entire left side over to the right side of the formula, which becomes 1 – (3/4 + 3/16 + 3/64 + …….). Step by step, it will become (1/4 – 3/16 – 3/64 – …..), then (1/16 – 3/64 – …..), then (1/64 – …..). Following the same sequence, it will become a 1/(multiples of 4), i.e., an inverse of an infinite number, which should be zero.

    This gives the verification of the equation.

    Am I right?

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  2. I enjoy number theory. My wife thinks I am strange that way. I am going to assume that is a win-win scenario.

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  3. Probably 75% of all the pictures I take are towards a vanishing point, what is being called convergence here. Yours are lovely :-)

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  4. Ooh maths . . . my head hurts

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  5. Pingback: weekly photo challenge: converge | Musings of a Random Mind

  6. Great post & def, Vlad. Happy Holidays to you both!
    del

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  7. Methinks I saw one of these before? Love shots like this!

    janet

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  8. love the mirrors in mirrors converging … I would have expected converging waterways from you…

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  9. That is amazing! I love it. :-)

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  10. Excellent interpretation of this week’s challenge. You took me right back to my school days with the math…which I seem to have forgotten how to work out with formulas :)

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  11. A clever interpretation Vlad :-)

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  12. amazing! why do these pictures make a curve in the distance?

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  13. That’s so cool. Maybe if math had been shown to us like this in school it would have been more fun and understandable for us math-challenged folks. :)

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  14. Great idea Vladi !!
    Great shots !
    Ciao ciao
    Max

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  15. Such an interesting photo, alongwith a mathematical formula….hahahaha….makes it so splendid…loved it..:)

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  16. I’m sorry to say that you lost me on the math but I enjoyed the great pictures of you and Johna and you and Johna and you and Johna…..ad infinitum.

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  17. mirrors always surprise me!

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