Egyptian Triangle

Geometry Revisited through Egyptian Triangle

One of the most famous Right Angle Triangles is 3-4-5 Right Angle Triangle. It is also known as Egyptian Triangle.

The origins of Right Triangle Geometry can be traced back to 3000 BC in Ancient Egypt. The Egyptians used special right triangles to survey land by measuring out 3-4-5 right triangles to make right angles. The Egyptians mostly understood right triangles in terms of ratios or what would now be referred to as Pythagorean Triplets.  The Egyptians also had not developed a formula for the relationship between the sides of a right triangle.

 It wasn’t until around 500 BC, when a Greek mathematician named Pythagoras discovered that there was a formula that described the relationship between the sides of a right triangle. This formula was known as the Pythagorean Theorem.

The relationship between 3, 4, and 5 is as ancient as Egypt, and as old as the Great

Pyramid of Giza. This powerful, glorious construction conceals deep mystical traditions that have begun to be popularized by archeological evidences too.

We know the mathematical importance of the relationships between the number 3, 4, and 5, but it was a well-kept secret in ancient times.

The classical numbers 3, 4, 5 are represented in the very structure of the Pyramid.

• The number One is the whole structure itself.

• The triangular faces represent the number 3.

• The square base is the number 4 and finally

• The four corners plus its apex complete the number 5.

These numbers had a profound mystical symbolism that becomes explicit in the explanations related to the Pythagorean triangle.

Mystically, the upright side, the perpendicular, is likened to the male; the base to the female and the hypotenuse to the child of both, and so Ausar [Osiris] may be regarded as the origin, Auset [Isis] as the recipient, and Heru [Horus] as perfected result. The short side of the right angle triangle is named “Ausar,” which corresponds to Osiris, the Father. The longer side is named “Auset,” corresponding to Isis, the Mother. And finally, the hypotenuse is called “Heru,” or Horus, the Son.

These names were assigned according to specific criteria: the upright side (3) is likened to the “male,” the Father Osiris. The horizontal base (4) is related to the “female,” the Mother Isis, and the hypotenuse (5) corresponds to the Son, Horus. The first is the “origin,” the second is the “recipient,” and the Son is the “result.”

Here in this blog post around seventy five questions exclusively on Egyptian Triangle are being uploaded for the quicker revision of almost all concepts/theorems of Geometry. 

Kindly see the above diagram and find the following:

(1) Area of the triangle ABC
(2) Inradius of the triangle ABC
(3) Circumradius of the triangle ABC
(4) Exradius on AB 
(5) Exradius on BC
(6) Exradius on CA 
(7) AD:CD
(8) DF
(9) DH
(10) AF
(11) Ratio of areas of Triangle AHD and DFC
(12) Area of triangle BDC
(13) XY
(14)YZ
(15) ZX
(16) Area of triangle XYZ
(17) Area of Triangle BXY
(18) Area of  Triangle AXD
(19) Area of Triangle DXY
(20) Area of Triangle YDC
(21) Area of Quadrilateral BXDY
(22) AX: XB
(23) BY:YC
(24) BE
(25) AE
(26) CE
(27) EK
(28) EJ
(29) AJ
(30) Ratio of areas of triangles AKE and triangle EJC.
(31) BL
(32) LL1
(33) LL2
(34) AL1
(35) Ratio of areas of triangles ALL2 and triangle LL1C
(36) AL
(37) CL
(38) AI: IN ; without finding the value of AI and IN
(39)  Now find AI
(40) and  IN
(41) BI
(42) IL
(43) AM
(44) MB
(45) BN:NC
(46) AL:CL
(47) AM:MB
(48) CI
(49) IM
(50) CI:IM
(51) Find the area of triangle LMN
(52) AP
(53 BQ
(54) CR
(55) Area of Triangle PQR
(56) Area of the Triangles whose sides are equal to AP, BQ and CR.
(57) Area of Triangle ARG
(58) AG:GP
(59) BG:GQ
(60) CG:GR
(61) Distance between Incentre and Circumcentre.
(62) Distance between Orthocentre and Circumcentre
(63) Distance between  Circumcentre and Centroid
(64) Distance between Centroid and Orthocentre.
(65) Distance between Incentre and Orthocentre
(66) Distance between Incentre and Centroid.
(67) Find the maximum possible area of a rectangle drawn in the triangle such that one angle of the rectangle is angle ABC.
(68) Find the area of a square drawn in the triangle such that one angle of the square is angle ABC.
(69) O is any point in the the triangle ABC. OU, OV, OW are three perpendiculars. Find the sum of OU, OV and OW.
(70) BCZ is an Equilateral Triangle and O1  is any point in the Triangle BZC. Find the sum of Three perpendiculars drawn on the three sides of the triangle from the point O1.


                                                                                                                     ( To be Continued)