{"id":1181,"date":"2017-11-18T03:32:54","date_gmt":"2017-11-18T03:32:54","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1181"},"modified":"2018-11-04T00:44:47","modified_gmt":"2018-11-04T00:44:47","slug":"fibonacci-numbers","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2017\/11\/18\/fibonacci-numbers\/","title":{"rendered":"Fibonacci Numbers"},"content":{"rendered":"

Fun Math for Girls
\n<\/span>By Kelly Tan<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

Do you like kittens? Bunnies? Guinea pigs? Puppies? They are cute and adorable. Wouldn\u2019t it be fun to have lots of them, with many of them reproducing more each month?<\/span><\/p>\n

That would be very exciting. So, let’s start counting how many pairs of bunnies we will have after each month. Suppose you started with a pair of baby female and male bunnies. After a month, they grow to adults. The next month, they produce a new pair of baby female and male bunnies. So, for the first 3 months, this is what you get. The symbol => represents the same pair of bunnies that exists from previous month, and | represents the birth of a new pair of bunnies.<\/span><\/p>\n

1st\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02nd\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a03rd
\n<\/span>Baby => Adult \u00a0=> Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Baby<\/span><\/span><\/p>\n

So, you will get 1 pair of baby bunnies in the first month, 1 pair of adult bunnies for the second month, and 1 pair each of baby and adult bunnies on the third month. Therefore, for the first 3 months you will have 1, 1, and 2 pairs of bunnies. Now what about the fourth month? You have:<\/span><\/p>\n

1st\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02nd\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a03rd<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a04th
\n<\/span>Baby => Adult => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult<\/span><\/span><\/p>\n

As you can see, the old adult pair continues to gives birth to a pair of baby bunnies, and the baby bunnies of the third month have become adults. So you have 3 pairs on the fourth month. And on the fifth month, what do you have?<\/span><\/p>\n

1st\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02nd\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a03rd<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a04th\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 5th
\n<\/span>Baby => Adult \u00a0=> Adult => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Baby
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Baby<\/span><\/span><\/p>\n

Exactly 5 pairs of bunnies! Now, try to figure out what do you get for the sixth month using the diagram above. Remember adult bunnies will give birth to a pair of baby bunnies, and baby bunnies will grow to be adults.<\/span><\/p>\n

1st\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02nd\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a03rd<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a04th\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 5th\u00a0 \u00a0 \u00a0\u00a0<\/span> \u00a0\u00a06th
\n<\/span>Baby => Adult \u00a0=> Adult => Adult => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby \u00a0=> Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Baby
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult => Adult => Adult
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Baby
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 |
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Baby => Adult<\/span><\/span><\/p>\n

There are 8 pairs of bunnies on the sixth month! So, how do you generalize this to additional months? Do you see a pattern?<\/span><\/p>\n

1st\u00a0 \u00a0 2nd\u00a0 \u00a0 3rd\u00a0 \u00a0 4th\u00a0 \u00a0 5th\u00a0 \u00a0 6th<\/span><\/p>\n

\u00a0 1\u00a0 \u00a0 \u00a0 \u00a01\u00a0 \u00a0 \u00a0 \u00a0 2\u00a0 \u00a0 \u00a0 \u00a0 3\u00a0 \u00a0 \u00a0 \u00a05\u00a0 \u00a0 \u00a0 \u00a0 \u00a08<\/span><\/p>\n

As you can see, on the third month, you inherit a pair of adults from the second month, and you get another pair of baby by birth from the adults. So you have 1+1=2 pairs. For the fourth month, you inherit 2 pairs from the third month, and you get another pair of babies from the adults again, but you don’t get one from the babies of the third month, so you have 2+1=3 pairs. On the fifth month, you inherit 3 pairs from the fourth month, and 2 pairs of adults, all grown from the third month, so you have 3+2=5 pairs. Now do you see the pattern.<\/span><\/p>\n

Yes, each month’s number is obtained by summing the numbers from the previous two months.<\/span><\/p>\n

Now try to do this to the tenth month, and see how many bunnies you have.<\/span><\/p>\n

1st\u00a0 \u00a0 2nd\u00a0 \u00a0 3rd\u00a0 \u00a0 4th\u00a0 \u00a0 5th\u00a0 \u00a0 6th\u00a0 \u00a0 7th\u00a0 \u00a0 8th\u00a0 \u00a0 9th\u00a0 \u00a0 10th
\n<\/span>\u00a0 1\u00a0 \u00a0 \u00a0 \u00a01\u00a0 \u00a0 \u00a0 \u00a0 2\u00a0 \u00a0 \u00a0 \u00a0 3\u00a0 \u00a0 \u00a0 \u00a05\u00a0 \u00a0 \u00a0 \u00a0 \u00a08\u00a0 \u00a0 \u00a0 \u00a013\u00a0 \u00a0 \u00a0 21\u00a0 \u00a0 \u00a034\u00a0 \u00a0 \u00a0 55<\/span><\/span><\/p>\n

On the 10th month, you will have 55 pairs of bunnies! Isn’t this exciting? This sequence of numbers is called the Fibonacci numbers.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Fun Math for Girls By Kelly Tan Do you like kittens? Bunnies? Guinea pigs? Puppies? They are cute and adorable. Wouldn\u2019t it be fun to have lots of them, with many of them reproducing more each month? That would be very exciting. So, let’s start counting how many pairs of bunnies we will have after […]<\/p>\n","protected":false},"author":1,"featured_media":1251,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1181","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/kellyfish.me\/wp-content\/uploads\/2017\/11\/CUTE-BUNNY-RABBITS-GLOSSY-POSTER-PICTURE-PHOTO-foot.jpg?fit=400%2C252&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1181","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/comments?post=1181"}],"version-history":[{"count":8,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1181\/revisions"}],"predecessor-version":[{"id":1288,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1181\/revisions\/1288"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media\/1251"}],"wp:attachment":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media?parent=1181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/categories?post=1181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/tags?post=1181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}