Lothar
USD 0.99
2.20for iPhone, iPad and more
Age Rating
لقطات الشاشة لـ Lothar
About Lothar
Lothar Collatz was born 6 July 1910 in Amsberg, Westphalia. During his
post-doctoral studies at at the age of 27, Collatz developed what is
now known as the Collatz Conjecture.
Simply stated, the Collatz Conjecture is as follows:
Given the function f, defined as:
| n÷2 if n ≡ 0 (mod 2)
f(n) = | 3×n + 1 if n ≡ 1 (mod 2)
|
for any positive starting integer n, repeated iterations of this
function will always lead to the cycle { 4, 2, 1 }. In other words,
repeated iterations of some starting number will always be eventually
decreasing and that there are no other cycles in the sequence besides
{ 4, 2, 1 }.
The Reverse function, f', is defined as the sequence moving backward
from an ending integer through to some initial starting integer that
would eventually arrive at the number entered through a series of
iterations. It is defined as follows:
| n×2 if n ≡ 0, 1, 2, 3, 5 (mod 6)
f'(n) = | (n - 1)÷3 if n ≡ 4 (mod 6) & "Previous" pressed
| n×2 if n ≡ 4 (mod 6) & "Multiply" pressed
This application was written by Jeffrey C. Jacobs and is Copyright ©2010
TimeHorse, LLC; source code is available upon request.
post-doctoral studies at at the age of 27, Collatz developed what is
now known as the Collatz Conjecture.
Simply stated, the Collatz Conjecture is as follows:
Given the function f, defined as:
| n÷2 if n ≡ 0 (mod 2)
f(n) = | 3×n + 1 if n ≡ 1 (mod 2)
|
for any positive starting integer n, repeated iterations of this
function will always lead to the cycle { 4, 2, 1 }. In other words,
repeated iterations of some starting number will always be eventually
decreasing and that there are no other cycles in the sequence besides
{ 4, 2, 1 }.
The Reverse function, f', is defined as the sequence moving backward
from an ending integer through to some initial starting integer that
would eventually arrive at the number entered through a series of
iterations. It is defined as follows:
| n×2 if n ≡ 0, 1, 2, 3, 5 (mod 6)
f'(n) = | (n - 1)÷3 if n ≡ 4 (mod 6) & "Previous" pressed
| n×2 if n ≡ 4 (mod 6) & "Multiply" pressed
This application was written by Jeffrey C. Jacobs and is Copyright ©2010
TimeHorse, LLC; source code is available upon request.
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تحديث لأحدث إصدار 2.20
Last updated on 05/04/2023
الإصدارات القديمة
Replaced the web viewer in the help window, fixed the placement of the reverse title, added the ability to force reload in the web browser by double-clicking the refresh button—but note, if clicked too fast, why the stop load is presented, it may cancel the page load. If you are having trouble double-clicking the refresh button because the stop load isn't disappearing in time or the time to second click is too short, you can now change the timeout in settings. Updated help.
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Version History
2.20
05/04/2023
Replaced the web viewer in the help window, fixed the placement of the reverse title, added the ability to force reload in the web browser by double-clicking the refresh button—but note, if clicked too fast, why the stop load is presented, it may cancel the page load. If you are having trouble double-clicking the refresh button because the stop load isn't disappearing in time or the time to second click is too short, you can now change the timeout in settings. Updated help.
2.11
25/11/2019
Ready for iOS 13
2.00.1
16/10/2016
* Numbers can now be of arbitrary length. Enter a million digits if you dare and see how long it takes to get to one.
* Actually, it takes no time at all, because now if you hold down the "Next" button, next is repeated until one is reached.
* So how do you know it got there? Well, now there's a ticker tape below the buttons to show you just how you got there. Scroll through the entire sequence.
* Can't see the end of the numbers in your list? Rotate your screen, Lothar now supports landscape mode.
* Sick of seeing all those old numbers and want to generate a new list? Click the trash can or clear button on larger displays.
* And now you can see the final, spiffy, new feature: the crisp, clear, new background issue of the man who came up with this awesome, unproven algorithm to bring any integer to one, Lothar Collatz, we thank you!
* Actually, it takes no time at all, because now if you hold down the "Next" button, next is repeated until one is reached.
* So how do you know it got there? Well, now there's a ticker tape below the buttons to show you just how you got there. Scroll through the entire sequence.
* Can't see the end of the numbers in your list? Rotate your screen, Lothar now supports landscape mode.
* Sick of seeing all those old numbers and want to generate a new list? Click the trash can or clear button on larger displays.
* And now you can see the final, spiffy, new feature: the crisp, clear, new background issue of the man who came up with this awesome, unproven algorithm to bring any integer to one, Lothar Collatz, we thank you!
1.01
25/10/2010
Lothar FAQ
انقر هنا لمعرفة كيفية تنزيل Lothar في بلد أو منطقة محظورة.
تحقق من القائمة التالية لمعرفة الحد الأدنى من المتطلبات Lothar.
iPhone
Requiere iOS 14.0 o posterior.
iPad
Requiere iPadOS 14.0 o posterior.
iPod touch
Requiere iOS 14.0 o posterior.
Lothar هي مدعومة على اللغات Inglés