I've Generated More Than 5000 Right Triangles with Integral Sides!

in steemstem •  7 years ago  (edited)

Pythagorean Triples

A Pythagorean triple is a right triangle that consists integral (whole number) sides and hypotenuse. According to Pythagoras, the sum of the squares of two perpendicular legs is equal to the square of the longest leg which is called the hypotenuse. That is,

a² + b² = c².

The well known Pythagorean triple is 3-4-5 triangle. That means the legs are 3 and 4 units and the hypotenuse is 5. The following are also known Pythagorean triples: 5-12-13, 7-24-25, 8-15-17, and many more.

As a mathematics enthusiast, I was curious how many Primitive Pythagorean triples are already discovered? Primitive Pythagorean triples are triangles with sides a, b, and c having no greatest common factor(GCF) other than 1. So, a 6-8-10 triangle is not counted because the sides are just multiples of 3-4-5, respectively.

I do not know what are the lengths of the sides of the Primitive Pythagorean triple that is already found out to be the one with the longest side. Answer.com states that it was the triangle with sides 77893200, 128189952, and 150000048 that is the largest so far.

Even though these don't make sense to other people, I had a curiosity that made me tabulate all the primitive Phytagorean triples by generating them with the use of VBA macros in excel. So far, I have generated 5003 primitive Pythagorean triples that have legs shorter than 50,000 units. I also include the VBA codes I used to generate these triangles.

These are the primitive Pythagorean triples that have hypotenuses less than 100.

No.a-b-cNo.a-b-cNo.a-b-cNo.a-b-c
13-4-559-40-41916-63-651336-77-85
25-12-13611-60-611020-21-291439-80-89
37-24-25712-35-371128-45-531548-55-73
48-15-17813-84-851233-56-651665-72-97

Last 100 Primitive Pythagorean Triples with legs less than 50,000 units.

No.a-b-cNo.a-b-c
490443392-24095-49633495445548-23325-51173
490543428-44525-62197495545560-21462-50362
490643473-48464-65105495645621-46060-64829
490743491-44620-62309495745732-30115-54757
490843608-47705-64633495845753-34504-57305
490943623-46864-64025495945784-46287-65105
491043680-49319-65881496045888-47905-66337
491143725-25172-50453496145895-46728-65497
491243804-45453-63125496245980-49539-67589
491343885-47532-64693496346008-27206-53450
491443896-47047-64345496446035-49028-67253
491543953-33896-55505496546169-47400-66169
491643976-48657-65585496646172-47235-66053
491743989-49820-66461496746272-48865-67297
491844023-45936-63625496846305-49712-67937
491944080-44799-62849496946443-48076-66845
492044147-48204-65365497046452-46565-65773
492144160-27387-51963497146560-23236-52036
492244187-37516-57965497246560-48191-67009
492344240-26718-51682497346604-21597-51365
492444268-47995-65293497446717-48756-67525
492544289-46600-64289497546835-41652-62677
492644310-33496-55546497646843-47124-66445
492744344-49617-66545497746844-47517-66725
492844384-35550-56866497846948-49155-67973
492944409-48880-66041497946991-49440-68209
493044415-45008-63233498047047-43896-64345
493144460-45731-63781498147121-47800-67121
493244473-38136-58585498247236-48477-67685
493344515-36612-57637498347276-38493-60965
493444555-47268-64957498447399-48480-67801
493544556-47333-65005498547628-49445-68653
493644671-49560-66721498647677-49164-68485
493744685-45668-63893498747712-32825-57913
493844736-45073-63505498847912-32175-57713
493944821-47940-65629498947955-49852-69173
494044829-31220-54629499048081-48200-68081
494144840-46671-64721499148138-32600-58138
494244932-48285-65957499248312-49735-69337
494345012-49915-67213499348336-39010-62114
494445087-48616-66305499448363-48884-68765
494545120-46009-64441499548400-25359-54641
494645220-20928-49828499648480-47399-67801
494745220-47619-65669499748600-49049-69049
494845308-49245-66917499848880-44409-66041
494945320-37791-59009499949155-46948-67973
495045347-45396-64165500049288-49335-69737
495145353-49296-66985500149539-45980-67589
495245495-47672-65897500249617-44344-66545
495345540-30749-54949500349621-49980-70429

How did I generate these?

Again, I have generated the triangles with the use of VBA Macro in Microsoft Excel. The codes I used are as follows. Try to generate them even upto 1,000,000 units length. Just change the ranges of a and b in my code! :)

Are you a math enthusiast too? Comment on this so that I can follow you! :)

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Wow Ser isa ka talagang lodi! hahahaha

Hahaha wala may lingaw shei. hahaha

Sir ikaw na talaga. 😊😊

hahaha. di tito boy, ikaw na!