Zeno's Paradox

This paradox lay unresolved for over 2000 years. See if you can Resolve and explain the situation.  Everybody loves a good race!!!!

Make sure to realize that Geogebra rounds the numbers, use this app to conceptualize that there wil always be a distance.

D(feet)=

See what the race looks like when the Hare catches up to where the Tortoise was

Finish Line

Finish Line

Finish Line

Starting Line

Starting Line

Every time the Hare catches up to where the Tortoise was, the Tortoise has moved forward.
So If the Hare can never catch up to the Tortoise, How come the Hare wins the race?

Show functions of the Hare and the Tortoise

Add slider to observe the speeds of the racers, and to see what actually happens in the race

Reset the Racers to the beginning

              The hare runs at 1 ft/sec. The Tortoise “runs” at .5 ft/sec.
The Tortoise gets a head start and is at 1ft before the Hare is allowed to start

Wait, so if it always takes time for the Hare to catch up to where the Tortoise was,
 won't the Tortoise aways have that same time to keep moving forward???

*Note-Geogebra rounds their numbers to at most 15 decimal places. If they didn't, you would be able to see that the Hair can never catch up to the Tortoise.
This is why, if you click enough times, it shows that both racers are at 2.  Without rounding, this won't happen.

TimeT(d) = (2 * (d - 1))
DistanceA(d) = d
d = 0 (slider from 0 to 3.5, step 0.1)
Hare = Vector((0, 1), (d, 1))
Turtoise = Vector((0, 0), ((0.5 * d) + 1, 0))
inputBox1 = Textfield(d)
PT: ((0.5 * d) + 1, 0)
AT: (d, 1)
xPT: x(PT)
xPA: x(AT)
Behind: xPT - xPA
A = Point(xAxis)
a = OrthogonalLine(A, xAxis)
B = (0, 0)
b = OrthogonalLine(B, Turtoise, xOyPlane)
C = Point(a)
D = Point(a)
c = Segment(C, D)
E = (0, 2)
F = (0, -1)
e = Segment(E, F)
f = Line(E, C)
g = Line(F, D)
h = false
i = false
text2: "The Hare is still behind the Tortoise " + Behind + " feet."
text1: "The Tortoise is " + xPT + " feet from the Starting Line. "
Time: d
text6: "It took the Hare " + Time + " seconds to get there. In " + Time + " seconds the Tortoise has now moved  " + Behind + " ft  further forward!!!!!"