Metallic ratios: Difference between revisions
→{{header|Perl}}
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After 615 iterations, the value of 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144 is stable to 256 decimal places.
</pre>
=={{header|Kotlin}}==
{{trans|Go}}
<lang scala>import java.math.BigDecimal
import java.math.BigInteger
val names = listOf("Platinum", "Golden", "Silver", "Bronze", "Copper", "Nickel", "Aluminium", "Iron", "Tin", "Lead")
fun lucas(b: Long) {
println("Lucas sequence for ${names[b.toInt()]} ratio, where b = $b:")
print("First 15 elements: ")
var x0 = 1L
var x1 = 1L
print("$x0, $x1")
for (i in 1..13) {
val x2 = b * x1 + x0
print(", $x2")
x0 = x1
x1 = x2
}
println()
}
fun metallic(b: Long, dp:Int) {
var x0 = BigInteger.ONE
var x1 = BigInteger.ONE
var x2: BigInteger
val bb = BigInteger.valueOf(b)
val ratio = BigDecimal.ONE.setScale(dp)
var iters = 0
var prev = ratio.toString()
while (true) {
iters++
x2 = bb * x1 + x0
val thiz = (x2.toBigDecimal(dp) / x1.toBigDecimal(dp)).toString()
if (prev == thiz) {
var plural = "s"
if (iters == 1) {
plural = ""
}
println("Value after $iters iteration$plural: $thiz\n")
return
}
prev = thiz
x0 = x1
x1 = x2
}
}
fun main() {
for (b in 0L until 10L) {
lucas(b)
metallic(b, 32)
}
println("Golden ration, where b = 1:")
metallic(1, 256)
}</lang>
{{out}}
<pre>Lucas sequence for Platinum ratio, where b = 0:
First 15 elements: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Value after 1 iteration: 1.00000000000000000000000000000000
Lucas sequence for Golden ratio, where b = 1:
First 15 elements: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
Value after 78 iterations: 1.61803398874989484820458683436564
Lucas sequence for Silver ratio, where b = 2:
First 15 elements: 1, 1, 3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119, 19601, 47321, 114243
Value after 44 iterations: 2.41421356237309504880168872420970
Lucas sequence for Bronze ratio, where b = 3:
First 15 elements: 1, 1, 4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564
Value after 34 iterations: 3.30277563773199464655961063373525
Lucas sequence for Copper ratio, where b = 4:
First 15 elements: 1, 1, 5, 21, 89, 377, 1597, 6765, 28657, 121393, 514229, 2178309, 9227465, 39088169, 165580141
Value after 28 iterations: 4.23606797749978969640917366873128
Lucas sequence for Nickel ratio, where b = 5:
First 15 elements: 1, 1, 6, 31, 161, 836, 4341, 22541, 117046, 607771, 3155901, 16387276, 85092281, 441848681, 2294335686
Value after 25 iterations: 5.19258240356725201562535524577016
Lucas sequence for Aluminium ratio, where b = 6:
First 15 elements: 1, 1, 7, 43, 265, 1633, 10063, 62011, 382129, 2354785, 14510839, 89419819, 551029753, 3395598337, 20924619775
Value after 23 iterations: 6.16227766016837933199889354443272
Lucas sequence for Iron ratio, where b = 7:
First 15 elements: 1, 1, 8, 57, 407, 2906, 20749, 148149, 1057792, 7552693, 53926643, 385039194, 2749201001, 19629446201, 140155324408
Value after 22 iterations: 7.14005494464025913554865124576352
Lucas sequence for Tin ratio, where b = 8:
First 15 elements: 1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449
Value after 20 iterations: 8.12310562561766054982140985597408
Lucas sequence for Lead ratio, where b = 9:
First 15 elements: 1, 1, 10, 91, 829, 7552, 68797, 626725, 5709322, 52010623, 473804929, 4316254984, 39320099785, 358197153049, 3263094477226
Value after 20 iterations: 9.10977222864644365500113714088140
Golden ration, where b = 1:
Value after 615 iterations: 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144</pre>
=={{header|Perl}}==
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