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#51 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-21 09:06:54
found it:The function
Hi anonimnystefy;
It's a nice expression!
Here is another expression: y = 0.5 sgn(x) (1 + sgn(abs(x) - 1)).
#52 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-02-08 15:00:20
#53 Re: This is Cool » [Fractal Spirograph] Fractal Roulette » 2012-02-01 08:30:48
Hi All,
A few images of successive zooming in have been added in the original post.
#54 Re: This is Cool » [Fractal Spirograph] Fractal Roulette » 2012-01-29 09:56:26
Hi anonimnystefy,
Thanks for the link.
Hi bobbym,
You're welcome.
Hi John,
What are the ratios between the circles?
The ratios used in the eight animated GIFs on my blog post are
3, 3, 2, 2, 2, 2, 2.5, and 2.75 respectively.
#56 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-01-27 07:19:12
Circle Rolling around Rolling Circle (3)
Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.
Circle Rolling around Rolling Circle (4)
Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.
#57 Re: Help Me ! » Make 1000 using 6 8's » 2012-01-12 02:22:05
1000 = 10^3
10 = 8 + sqrt( sqrt(8+8) )
3 = sqrt(8 + 8/8)
#58 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-01-09 13:06:46
Hi anonimnystefy,
Thank you for your appreciation.
Hi bobbym,
There are some new features in GeoGebra 4.0.
#59 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-01-09 12:42:12
Circle Rolling around Rolling Circle (2)
Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.
#60 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-01-09 12:29:58
Can you do the logarhythm of the distances to make it possible to see this one:
Make the big moving circle go around the sun, like Earth. And then make the tiniest circle go around the Earth like the moon.
Don't use logs at first but one is 94 million miles and the other one is a quarter of a million, or something like that so it might not be easy to view it since 4 times 94+/- is around 376 for the ratio of the earth and moon circle sizes. Now looking down at the solar system from the north star, the Earth goes CCW and the moon also goes CCW, the last time I remember.`
Hi John,
Please see the attached image sun_earth_moon_d2_0.png for the orbit of the moon around the sun.
The parameter values I use:
The radius of the Sun = 69.55 × 10^4 km.
The radius of the Earth = 0.6371 × 10^4 km.
The radius of the Moon = 0.17371 × 10^4 km.
The average distance from the Earth to the Sun = 14959.787 × 10^4 km.
The average distance from the Moon to the Earth = 38.5 × 10^4 km.
The period of the Earth's orbit around the Sun = 365.2422 days.
The period of the Moon's orbit around the Earth = 27.32 days.
Earth's rotation period = 1 day.
Moon's rotation period = 27.32 days.
Suppose P2 is a point which is (d2 × 10^4 km) away from the center of the Moon
and is fixed relative to the Moon.
Please see images sun_earth_moon_d2_200.jpg ~ sun_earth_moon_d2_4000.jpg
for the orbits of P2 around the sun with some different d2 values.
Suppose P1 is a point which is (d1 × 10^4 km) away from the center of the Earth
and is fixed relative to the Earth. P is the midpoint between P1 and P2.
Please see the following images for the orbits of P around the sun with some d1 and d2 values:
sun_earth_moon_d1_3000_d2_5000.jpg,
sun_earth_moon_d1_5000_d2_1000.jpg,
sun_earth_moon_d1_5000_d2_3000.jpg.
#61 This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2011-12-08 22:49:33
- benice
- Replies: 19
Circle Rolling around Rolling Circle (1)
Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.
Circle Rolling around Rolling Circle (2)
Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.
Circle Rolling around Rolling Circle (3)
Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.
Circle Rolling around Rolling Circle (4)
Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.
#63 This is Cool » Rolling Regular Polygons around a Circle » 2011-11-21 01:41:30
- benice
- Replies: 5
#64 Re: This is Cool » sums of power sequences » 2011-11-17 03:25:29
#65 Re: Help Me ! » max. value » 2011-11-06 11:14:04
Thanks benice you are Right.
But can you explain me Why we take {d(P,A) - d(P,C)} + {d(P,B) - d(P,D)}
We also take {d(P,A) - d(P,D)} + {d(P,B) - d(P,C)}
The inequality |d(P,A) - d(P,C)| ≤ d(A,C) holds with equality
iff P = A or P = C or P lies on line AC, but not on segment AC.
The inequality |d(P,B) - d(P,D)| ≤ d(B,D) holds with equality
iff P = B or P = D or P lies on line BD, but not on segment BD.
Hence |f(x,y)| attains its maximum value when (x,y) is the point of intersection of
(line AC \ segment AC) and (line BD \ segment BD). (See image1.)
Taking {d(P,A) - d(P,D)} + {d(P,B) - d(P,C)} will just get an upper bound of |f(x,y)|,
not the maximum value of |f(x,y)|. (See image2.)
Hi benice;
What does d(P,A) do? Can you post it?
The distance between P and A.
#66 Re: Help Me ! » max. value » 2011-11-05 12:39:13
Consider points A(0,1), B(3,4), C(0,0), D(1,0), P(x,y).
We have
|f(x,y)|
= |d(P,A) + d(P,B) - d(P,C) - d(P,D)|
= |d(P,A) - d(P,C) + d(P,B) - d(P,D)|
≤ |d(P,A) - d(P,C)| + |d(P,B) - d(P,D)|
≤ d(A,C) + d(B,D)
= 1 + sqrt(20)
= 1 + 2 sqrt(5) ...... Ans.
#67 Re: This is Cool » [Crazy Math Picture] Man Giving Three Middle Fingers » 2011-11-05 02:08:41
Hi bob bundy;
Benice: Nice pic but surely it's a woman not a man. That looks like a bra to me and a very narrow waist!
You have a very good imagination.
It's a part of a mathematical image found by experiment.
What it looks like varies from person to person.
#68 Re: This is Cool » [Crazy Math Picture] Man Giving Three Middle Fingers » 2011-11-03 17:25:39
Hi bobbym;
Looks like two eyes staring upward with a big nose between them.
The big nose is the third middle finger. Just Kidding.
I guess it is my old war injury. Got hit in the eyeballs with a mortar shell back in 43.
I'm sorry to hear that. Mortars are dangerous. I have some experience with 81mm mortars.
#69 Re: This is Cool » [Crazy Math Picture] Man Giving Three Middle Fingers » 2011-11-03 09:11:53
Hi bobbym;
It's at the top of the picture.
#70 This is Cool » [Crazy Math Picture] Man Giving Three Middle Fingers » 2011-11-02 05:38:16
- benice
- Replies: 40
#71 Re: This is Cool » a circle algorithm that doesn't use pi » 2011-10-27 04:05:12
Hi circlemaker;
Awesome! Thank you so much for doing this work and sharing it.
#72 Re: Introductions » Greetings » 2011-10-21 05:09:44
Hi TheGimp;
You are a good grandpa!
#73 Re: This is Cool » Fractals in html5 » 2011-10-21 04:39:53
#74 Re: This is Cool » The best known packings of equal circles in a circle » 2011-10-21 04:33:55
Hello and thank you for the link! 
#75 This is Cool » Superposing Star Polygons » 2011-10-18 19:45:18
- benice
- Replies: 1
Hi All!
Regular Star Polygon {n/k}: Formulas and Examples
Superposing Star Polygons (1): n = 32, k = 1 ~ 15
Superposing Star Polygons (2): n = 3 ~ 40
Thank you for watching and best regards.
