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Friday, April 12

Saturday, March 2

  1. page Slope of a reflected line edited If a line with slope a (in the plane) is reflected through another line with slope b, then the ima…
    If a line with slope a (in the plane) is reflected through another line with slope b, then the image line has slope c,
    where c = (a*b^2-a+2*b)/(-b^2+1+2*b*a).
    In this GeoGebra worksheet, the blue line is the reflected image of the red line through the black line. Adjust the sliders to change the slopes of the lines.

    (view changes)
    8:35 am

Sunday, January 27

  1. file sine-series.pdf uploaded
    10:33 pm

Monday, December 31

  1. page Constructing the square root edited This applet demonstrates the standard ruler and compass construction for the square root of a numb…
    This applet demonstrates the standard ruler and compass construction for the square root of a number. Drag the point C to see how it works.
    (view changes)
    10:43 am

Sunday, December 16

  1. page Solutions to sin(x) = c edited The equation sin(x) = c has two solutions in the interval [0°, 360°) when -1 < c < 1. If c =…
    The equation sin(x) = c has two solutions in the interval [0°, 360°) when -1 < c < 1. If c = 1 or c = -1 then there is only one solution in this interval.
    Drag the slider to visualize these solutions on the unit circle.

    (view changes)
    11:20 am

Saturday, September 29

  1. page Shoelace problem edited ... You are walking from one end of an airport terminal to the other. The airport has several movi…
    ...
    You are walking from one end of an airport terminal to the other. The airport has several moving walkways, and you need to stop to tie your shoelace. Assuming you want to get to the other end as quickly as possible, is it better to tie your shoelace while you are on a moving walkway or while you are between walkways?
    Some of my friends who work at the airport had more practical suggestions, such as "call a cart" or "wear loafers", but I am more interested in the mathematical question. The worksheet below shows a time-distance graph for each of the two scenarios. The green line shows what happens if you tie your shoelace while you are on the moving walkway, and the red line shows what happens if you tie your shoelace while you are between walkways.
    Conclusion: It is quicker to tie your shoelace while you are on a moving walkway.
    {airport shoelace.ggb}
    (view changes)
    8:29 am
  2. page Shoelace problem edited Here is an intriguing real world math problem that was posed by Terry Tao. You are walking from o…
    Here is an intriguing real world math problem that was posed by Terry Tao.
    You are walking from one end of an airport terminal to the other. The airport has several moving walkways, and you need to stop to tie your shoelace. Assuming you want to get to the other end as quickly as possible, is it better to tie your shoelace while you are on a moving walkway or while you are between walkways?
    Some of my friends who work at the airport had more practical suggestions, such as "call a cart" or "wear loafers", but I am more interested in the mathematical question. The worksheet below shows a time-distance graph for each of the two scenarios. The green line shows what happens if you tie your shoelace while you are on the moving walkway, and the red line shows what happens if you tie your shoelace while you are between walkways.
    {airport shoelace.ggb}

    (view changes)
    8:27 am

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