# data[].attributes.headline
note: this connects to "Dandelion" from previous tier, this likely is not a golden clue

# data[].attributes.subject
note: this connects to "Dandelion" from previous tier, this likely is not a golden clue

# data[].attributes.body
Dande + Lion (leo) found in previous tier lead to yellow/gold

# data[].attributes.body
Tier 1A - 1064

Tier 1B - lxxix (79)

Tier 1C - 5f137s2

Tier 1D - 0vif0rm

Tier 1E - cacoiii

Tier 1F - vit3llus

Tier 2ABC - viold

Tier 2DEF - evivi

# data[].attributes.body
6 greek crosses

6 latin crosses

6 saint peter crosses

# data[].attributes.body
Common Pythagorean triples

Main article: Pythagorean triple

There are several Pythagorean triples which are well-known, including those with sides in the ratios:

one of these is

5 12 13

# data[].attributes.attachment_link.readable_text
Position of some special triangles in an Euler diagram of types of triangles, using the definition that isosceles triangles have at least two equal sides, i.e. equilateral triangles are isosceles.

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°-45°-90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods.

Special angle-based triangles inscribed in a unit circle are handy for visualizing and remembering trigonometric functions of multiples of 30 and 45 degrees.

Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or radians, is equal to the sum of the other two angles.

The side lengths are generally deduced from the basis of the unit circle or other geometric methods. This approach may be used to rapidly reproduce the values of trigonometric functions for the angles 30°, 45°, and 60°.

Special triangles are used to aid in calculating common trigonometric functions, as below:

The 45°-45°-90° triangle, the 30°-60°-90° triangle, and the equilateral/equiangular (60°-60°-60°) triangle are the three Möbius triangles in the plane, meaning that they tessellate the plane via reflections in their sides; see Triangle group.

45° - 45° - 90° triangle

Set square shaped as 45° - 45° - 90° triangle

The side lengths of a 45° - 45° - 90° triangle

45° - 45° - 90° right triangle of hypotenuse length 1.

In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or π radians. Hence, the angles respectively measure 45° (), 45° (), and 90° (). The sides in this triangle are in the ratio 1 : 1 : , which follows immediately from the Pythagorean theorem.

Triangles with these angles are the only possible right triangles that are also isosceles triangles in Euclidean geometry. However, in spherical geometry and hyperbolic geometry, there are infinitely many different shapes of right isosceles triangles.

30° - 60° - 90° triangle

Set square, shaped as 30° - 60° - 90°° triangle

The side lengths of a 30°-60°-90° triangle

30° - 60° - 90° right triangle of hypotenuse length 1.

This is a triangle whose three angles are in the ratio 1 : 2 : 3 and respectively measure 30° (), 60° (), and 90° (). The sides are in the ratio 1 : : 2.

The proof of this fact is clear using trigonometry. The geometric proof is:

Draw an equilateral triangle ABC with side length 2 and with point D as the midpoint of segment BC. Draw an altitude line from A to D. Then ABD is a 30°-60°-90° triangle with hypotenuse of length 2, and base BD of length 1.

The fact that the remaining leg AD has length follows immediately from the Pythagorean theorem.

The 30°-60°-90° triangle is the only right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows on from the fact that if α, , are the angles in the progression then the sum of the angles = 180°. After dividing by 3, the angle must be 60°. The right angle is 90°, leaving the remaining angle to be 30°.

Right triangles whose sides are of integer lengths, with the sides collectively known as Pythagorean triples, possess angles that cannot all be rational numbers of degrees. (This follows from Niven's theorem.) They are most useful in that they may be easily remembered and any multiple of the sides produces the same relationship. Using Euclid's formula for generating Pythagorean triples, the sides must be in the ratio

There are several Pythagorean triples which are well-known, including those with sides in the ratios:

The 3 : 4 : 5 triangles are the only right triangles with edges in arithmetic progression. Triangles based on Pythagorean triples are Heronian, meaning they have integer area as well as integer sides.

The possible use of the 3 : 4 : 5 triangle in Ancient Egypt, with the supposed use of a knotted rope to lay out such a triangle, and the question whether Pythagoras' theorem was known at that time, have been much debated. It was first conjectured by the historian Moritz Cantor in 1882. It is known that right angles were laid out accurately in Ancient Egypt; that their surveyors did use ropes for measurement; that Plutarch recorded in Isis and Osiris (around 100 AD) that the Egyptians admired the 3 : 4 : 5 triangle; and that the Berlin Papyrus 6619 from the Middle Kingdom of Egypt (before 1700 BC) stated that "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." The historian of mathematics Roger L. Cooke observes that "It is hard to imagine anyone being interested in such conditions without knowing the Pythagorean theorem." Against this, Cooke notes that no Egyptian text before 300 BC actually mentions the use of the theorem to find the length of a triangle's sides, and that there are simpler ways to construct a right angle. Cooke concludes that Cantor's conjecture remains uncertain: he guesses that the Ancient Egyptians probably did know the Pythagorean theorem, but that "there is no evidence that they used it to construct right angles".

The following are all the Pythagorean triple ratios expressed in lowest form (beyond the five smallest ones in lowest form in the list above) with both non-hypotenuse sides less than 256:

Isosceles right-angled triangles cannot have sides with integer values, because the ratio of the hypotenuse to either other side is and cannot be expressed as a ratio of two integers. However, infinitely many almost-isosceles right triangles do exist. These are right-angled triangles with integer sides for which the lengths of the non-hypotenuse edges differ by one. Such almost-isosceles right-angled triangles can be obtained recursively,

Alternatively, the same triangles can be derived from the square triangular numbers.

A Kepler triangle is a right triangle formed by three squares with areas in geometric progression according to the golden ratio.

The Kepler triangle is a right triangle whose sides are in geometric progression. If the sides are formed from the geometric progression a, ar, ar ² then its common ratio r is given by r = where φ is the golden ratio. Its sides are therefore in the ratio . Thus, the shape of the Kepler triangle is uniquely determined (up to a scale factor) by the requirement that its sides be in geometric progression.

The 3-4-5 triangle is the unique right triangle (up to scaling) whose sides are in arithmetic progression.

The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle

Let

be the side length of a regular decagon inscribed in the unit circle, where is the golden ratio. Let

be the side length of a regular hexagon in the unit circle, and let

be the side length of a regular pentagon in the unit circle. Then , so these three lengths form the sides of a right triangle.[10] The same triangle forms half of a golden rectangle. It may also be found within a regular icosahedron of side length : the shortest line segment from any vertex to the plane of its five neighbors has length , and the endpoints of this line segment together with any of the neighbors of form the vertices of a right triangle with sides , , and .[11]

# data[].attributes.attachment_link.description
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°-45°-90°. This is called an "angle-based" right triangle.

# data[].attributes.body
1404E210DDFD - 4FA5E227933D2 - 1A3DC

"Keep it simple"

12 digits

13 digits

5 digits

# data[].attributes.body
Might be a "diamond" clue. QR code found in the image led to the url above with this record on it.

Theory: Can't find exact image online, but found similar one not turned in a 90 deg angle (may be nothing)

# data[].attributes.headline
Tier 1 E - THE_FINALS_OSPUZE_AD_bonus_candy.jpg (UNSOLVED)

# data[].attributes.subject
Tier 1 E - THE_FINALS_OSPUZE_AD_bonus_candy.jpg (UNSOLVED)

# data[].attributes.body
FIND PSW: XXXX-XX-XX

No such password was used in any previous tiers.

# data[].attributes.headline
Tier 1 F bonus - THE_FINALS_NamaTama_Concept_0.1.png (UNSOLVED)

# data[].attributes.subject
Tier 1 F bonus - THE_FINALS_NamaTama_Concept_0.1.png (UNSOLVED)

# data[].attributes.body
313.82.444.84.576.110.112.264.231.292.444.232 code (repeated 3 times)

# data[].attributes.headline
6 months later in Discord throws a potential connection with "hard"

# data[].attributes.subject
6 months later in Discord throws a potential connection with "hard"

# data[].attributes.body
missing A

Theory: Leads to a "diamond" clue not "golden"

# data[].attributes.body
During this tier on January 4th, 2023, Rob posted the following message regarding the Van Morrison clues:

To be honest it's actually not just "hard", it's more or less impossible, when I put it in there I actually thought "NO ONE will EVER find this link"... I still don't think anyone will figure it out, but it was VERY impressive that RHB found the SECOND meaning of VM... but if anyone find the actual link between the second VM and the actual password... I will send you an unique THE FINALS gift... ._.

# data[].attributes.body
5 songs were titles of the main images in that tier.

“Brown Eyed Girl”

“Red Sports Caracter”  (1. “acter” removed leads to Van Morrison song 2. H is missing which could be another diamond clue such as “o” missing in “burrow”)

“Into The Mystic”

“Beside You”

“Keep It Simple”

# data[].attributes.body
1. Solve using that Tiers' knowledge to remove as "golden" or "diamond" clue

2. Connect to other "diamond" clues to remove as a "golden" clue for this Level.

3. Connect to other "golden" clues and solve the final tier of Level 2 - The Promise

# data[].attributes.headline
Tier 1 F - THE_FINALS_CB2_Guns_and_Namas.png (UNSOLVED)

# data[].attributes.subject
Tier 1 F - THE_FINALS_CB2_Guns_and_Namas.png (UNSOLVED)

# data[].attributes.body
Posted by Rob as said the solution was they are communes of Dande.

https://en.wikipedia.org/wiki/Dande

# data[].attributes.headline
Tier 1 E - THE_FINALS_OSPUZE_AD_bonus_candy.jpg (UNSOLVED)

# data[].attributes.subject
Tier 1 E - THE_FINALS_OSPUZE_AD_bonus_candy.jpg (UNSOLVED)

# data[].attributes.body
Numbers with periods: 13.0.10.3.3 (last number doesn't have one)

Theory: Mayan Date format for January 1st 2023

# data[].attributes.headline
Tier 1 D - Keep_It_Simple.jpg (UNSOLVED)

# data[].attributes.subject
Tier 1 D - Keep_It_Simple.jpg (UNSOLVED)

# data[].attributes.body
Only thing of note is that "day" is repeated 3 times in his message.

# data[].attributes.headline
Tier 1 D - Keep_It_Simple.jpg (UNSOLVED)

# data[].attributes.subject
Tier 1 D - Keep_It_Simple.jpg (UNSOLVED)

# data[].attributes.body
Found in the footer. Rob acknowledged in a Discord message.

Theory: message is in XXXX-XX-XX format signified by the 2 dashes

# data[].attributes.body
Color Legend & Tips:
Blue: Embark Offical Images/Statements
Green: Clues From Embark Images
Orange: Our Investigations.
Red: Paths that are either confirmed or likely. 


If you double click on the background, it will make a post there. 