1. Around the World: Islands of Biological Wonder Kristian Wilks - Pre Calc. 11A - 10/1/12

2. The Trip Home: St. Clair Shores, MI – Coordinates: 42.4969° N (42°30’ N), 82.8889° W (82°53’ W) Destination 1: Santa Cruz Island, Galapagos – Coordinates: 1.3861° N (1°23’ N), 91.9197° W (91°49’ W) Destination 2: Antananarivo, Madagascar – Coordinates: 18.9386° S (18°56’ S), 47.5214° E (47°31’ E) Destination 3: Sipadan Island, Malaysia – Coordinates: 4.1147° N (4°7’ N), 118.6288° E (118°38’ E)

3. Equations Used Spherical Law of Cosines – cos(n) = cos(a)*cos(b) + sin(a)*sin(b)*cos(N) Arc Length of Circle – Distance = (n/360)*2*pi*radius of Earth n is an angle Radius of Earth = 3960 miles

4. 1 st Trip – Santa Cruz Island, Galapagos

5. Why Santa Cruz Island, Galapagos? Santa Cruz Island is the main town of the Galapagos. Like the rest of the Galapagos, it is home to unique and exotic plants and animals which cannot be found anywhere on Earth. Imagine being able to walk along side amazing animals such as tortoises while exploring the island. The ocean view along with the natural surroundings make for beautiful scenery that cannot be matched as well. It is an amazing place for those who love wild life and for those who love the mysteries that life holds.

6. 1 st Trip – Calculations Distance 1: St. Clair Shores, MI (S) to Santa Cruz Island, Galapagos (G) 89°60’ - 1°23’ s = 88°37’ 89°60’ - 42°30’ g = 47°30’

7. 1 st Trip – Calculations 91°49’ - 82°53’ N = 8°56’ cos n = cos(s)*cos(g)+sin(s)*sin(g)*cos(N) cos n = cos(47°30’)*cos(88°37’)+sin(47°30’)*sin(88°37’)*cos(8°56’) cos n = 0.744503299071 n = 41.8835461944° Distance 1 = (n/360)*2*pi*r Distance 1 = (41.8835461944 /360)*2*pi*3960 miles Distance 1 = 2,895 miles

8. 2 nd Trip – Antananarivo, Madagascar

9. Why Antananarivo, Madagascar? Antananarivo is the capital of Madagascar and the center of human life here. Though the city itself is not the focus, the island of Madagascar is filled with exotic animals and plants that will amaze the minds of the tourists who travel there. The lemurs and strange reptiles that call Madagascar home are the main reason to visit providing experiences and sights that are unparalleled by any other place on Earth.

10. 2 nd Trip – Calculations Distance 2: Santa Cruz Island, Galapagos (G) to Antananarivo, Madagascar (M) 89°60’ + 18°56’ g = 108°56’ 89°60’ - 1°23’ m = 88°37’

11. 2 nd Trip – Calculations 91°49’ + 47°31’ N = 139°20’ cos n = cos(g)*cos(m)+sin(g)*sin(m)*cos(N) cos n = cos(88°37’)*cos(108°56’)+sin(88°37’)*sin(108°56’)*cos(139°20’) cos n = -0.725177359314 n = 136.483604035° Distance 2 = (n/360)*2*pi*r Distance 2 = (136.483604035 /360)*2*pi*3960 miles Distance 2 = 9,433 miles

12. 3 rd Trip – Sipadan Island, Malaysia

13. Why Sipadan Island, Malaysia? Sipadan Island is off the coast of Borneo and belongs to Malaysia. Although the island itself is fascinating, the real reason to visit is the sea life surrounding the islands. Taking a dive down around the reefs provides for an up close view of the stunning sea life that is unique to the area. Imagine being able to swim along side sea turtles and other amazing fish while viewing the beautiful reefs below! It is the perfect way to get away from home and unwind!

14. 3 rd Trip – Calculations Distance 3: Antananarivo, Madagascar (M) to Sipadan Island, Malaysia (I) 89°60’ - 4°7’ m = 85°53’ 89°60’ +18°56’ i =108°56’

15. 3 rd Trip – Calculations 118°38’ - 47°31’ N = 71°7’ cos n = cos(m)*cos(i)+sin(m)*sin(i)*cos(N) cos n = cos(108°56’)*cos(85°53’)+sin(108°56’)*sin(85°53’)*cos(71°7’) cos n = 0.328765647938 n = 70.8061275329° Distance 3 = (n/360)*2*pi*r Distance 3 = (70.8061275329 /360)*2*pi*3960 miles Distance 3 = 4,894 miles

16. 4 th Trip – Back Home

17. 4 th Trip – Calculations Distance 4: Sipadan Island, Malaysia (I) to St. Clair Shores, MI (S) 89°60’ - 42°30’ i = 47°30’ 89°60’ - 4°7’ s = 85°53’

18. 4 th Trip – Calculations 360 - (118°38’+82°53’) N = 158°29’ cos n = cos(i)*cos(s)+sin(i)*sin(s)*cos(N) cos n = cos(85°53’)*cos(47°30’)+sin(85°53’)*sin(47°30’)*cos(158°29’) cos n = -0.635685246581 n = 129.470826473° Distance 3 = (n/360)*2*pi*r Distance 3 = (129.470826473 /360)*2*pi*3960 miles Distance 3 = 8,948 miles

19. Picture Sources Picture of Earth: – http://www.google.com/imgres?q=picture+of+earth&um=1&hl=en&safe=active&sa=N&biw=1092&bih=499&tbm=isch&tbn id=j8-LMYuOxLVKxM:&imgrefurl=http://blenderartists.org/forum/showthread.php%3F229511-Clouds-From-the-view-of- space&docid=zWazXI2pLPreaM&imgurl=http://gkbsolarsystem.wikispaces.com/file/view/earth2_medium.jpg/116480707/ear th2_medium.jpg&w=1440&h=1540&ei=zKRoUIK1B6XzyAHKhIGICA&zoom=1&iact=hc&vpx=96&vpy=123&dur=797&h ovh=232&hovw=217&tx=133&ty=138&sig=117730032865579301503&page=2&tbnh=148&tbnw=128&start=12&ndsp=16 &ved=1t:429,r:5,s:12,i:132 Picture of Santa Cruz Tortoise: – http://www.google.com/imgres?q=santa+cruz+island+galapagos&start=101&um=1&hl=en&safe=active&sa=N&biw=1092& bih=499&tbm=isch&tbnid=y0btuWZpH0Be1M:&imgrefurl=http://matthewmeierphoto.photoshelter.com/image/I0000DWN3 GoQDWZU&docid=KXZCwCFPvNz3JM&imgurl=http://cdn.c.photoshelter.com/img- get/I0000DWN3GoQDWZU/s/750/750/galapagos-giant-tortoise-wild- 013065.jpg&w=750&h=498&ei=wJ1oUMfVHcaJywG5zYG4BQ&zoom=1&iact=rc&dur=310&sig=11773003286557930150 3&page=8&tbnh=153&tbnw=215&ndsp=15&ved=1t:429,r:12,s:101,i:93&tx=135&ty=33 Picture of Madagascar Lemur: – http://www.google.com/imgres?q=madagascar&um=1&hl=en&safe=active&biw=1092&bih=499&tbm=isch&tbnid=_ztuCUz rlwVL3M:&imgrefurl=http://animals.howstuffworks.com/mammals/lemurs-live-in-madagascar1.htm&docid=3gKl6- K4zcFVkM&imgurl=http://static.ddmcdn.com/gif/lemurs-live-in-madagascar- 4.jpg&w=400&h=300&ei=_I5oUMq_LomkyQG4zoDADQ&zoom=1&iact=hc&vpx=657&vpy=4&dur=1510&hovh=195&ho vw=260&tx=129&ty=60&sig=117730032865579301503&page=5&tbnh=141&tbnw=212&start=61&ndsp=16&ved=1t:429,r: 3,s:61,i:280

20. Picture Sources Picture of Sipadan Island Sea Turtle: – http://www.google.com/imgres?q=sipadan+island+malaysia&um=1&hl=en&safe=active&sa=N&rlz=1C1TSNO_enUS463US 463&biw=1092&bih=499&tbm=isch&tbnid=yQ1lmhxXFm6nrM:&imgrefurl=http://www.divetrip.com/phot0307e.htm&doci d=TcYhEvkzhhRtM&imgurl=http://www.divetrip.com/photos/sipturtle4.jpg&w=640&h=480&ei=bJtoUMONL9KFyQGA0ID ACA&zoom=1&iact=hc&vpx=342&vpy=64&dur=1876&hovh=195&hovw=260&tx=147&ty=150&sig=1177300328655793 01503&page=4&tbnh=144&tbnw=213&start=40&ndsp=13&ved=1t:429,r:1,s:40,i:211 Picture of St. Clair Shores Nautical Mile Sign: – http://www.google.com/imgres?q=St.+clair+shores+michigan&um=1&hl=en&safe=active&sa=N&biw=1092&bih=499&tbm=i sch&tbnid=zSIbus1PMWQrsM:&imgrefurl=http://localism.com/mi/saint_clair_shores/the_nautical_mile&docid=W0rP28ys13 SOSM&imgurl=http://localism.com/system/s3_buckets/localism-production-image- store/photo_c5191b9da1ae4497cd5c0d10b82b6d950d3e46c7a528caaeb6a6bfdcb8141bd3.jpg&w=1024&h=768&ei=fJ1oUJP DDcHIyQGM6YGAAQ&zoom=1&iact=rc&dur=1&sig=117730032865579301503&page=1&tbnh=143&tbnw=176&start=0&nds p=10&ved=1t:429,r:5,s:0,i:89&tx=242&ty=320

21. THE END!