Is it possible to determine the approximate height of a bamboo culm by measuring its girth or diameter? Absolutely! In fact, bamboo is the only plant that exhibits a direct mathematical relationship between the circumference of its culm and both the internode length and overall height. This unique characteristic not only allows for accurately determining the culm height, but also aids in identifying the specific bamboo species.

Identification of Bamboo Species by Mathematical Relationship

In 1941, Dickason proposed an intriguing theory regarding the identification of bamboo species. He introduced a diagnostic method that involves examining the mathematical relationship between the circumference or culm girth, denoted as "C," at a specific height of 1.35 meters (4.5 feet) above the ground, and the length of the internode, denoted as "L," located at the same elevation.

Dickason justified the selection of 1.35 meters as the designated height by considering practical factors. This particular elevation is easily reachable, eliminating the need for any excessive effort. Furthermore, it is typically free from persistent overlapping sheaths, ensuring unobstructed measurement. Most importantly, this method does not require cutting the culm, thus preserving the bamboo plant in its entirety.

He gives the following relations C/L taken in some species:

Applying this theory to the species Guadua angustifolia would result in a C/L reaction of 1.56

Circumference at 1.35 m (C = 33.6 cm) divided by the internode length at same height (L = 21.5 cm)

The Mathematical Relation between Culm Height and Girth in Bamboo

In traditional Japanese practices, there exists a mathematical relationship between the height of the bamboo culm and the girth or circumference of the culm measured at eye level. However, it is also acceptable to measure the culm girth at breast level, as the difference between the two measurements is typically negligible.

In Japan, buyers of bamboo culms follow a specific method to determine the culm length. They multiply the culm girth at eye level by a constant of 60. This procedure is applicable to culms over 7 cm in diameter. Alternatively, some buyers multiply the culm diameter by the value of "pi" (3.14) and then by 60.

This calculation method is commonly employed to assess the quality of the culms. If the calculated length matches or exceeds the actual culm length, it signifies a culm of exceptional quality. Conversely, if the calculated length is shorter, it indicates a culm of lower quality and subsequently lower cost.

The specific constant used in this calculation method varies depending on the bamboo species. In Colombia, Oscar Hidalgo and Prof. Jorge Escobar conducted experiments with Guadua angustifolia, cutting approximately 60 culms. They meticulously measured each culm to determine the constant required to calculate an approximate culm height for this species. The resulting constant was determined to be 58.2.

To illustrate this calculation with an example, if the culm girth at breast level measures 0.37 m, the estimated culm height would be approximately 0.37 x 58.2 = 21.3 m

If one were to use the culm diameter instead of the girth, the height calculation would be as follows: 0.117 x 3.14 x 58.2 = 21.3 m

The Diminishing Size of Giant Bamboos Over Time

Giant Bamboo Colonial Time — Giant Bamboo - *Courtesy:* *Save Trees-"Save World"*

Based on the mathematical relation that allows us to estimate the height of Guadua bamboo culms, we can calculate the approximate height of these culms during Columbus' arrival in the Americas in 1502. By considering the available information about the dimensions of their circumferences at that time, we can gain insights into their sizes.

For instance, in 1526, Oviedo, a Spanish historian, described the circumferences of bamboo species in Ecuador. He stated, "Among all types of bamboo, there are some that are extremely large, with internodes as thick as a heavy man's thigh and a circumference of three palms or more" (Patino 1975). Here, a "palm" refers to an old Spanish measurement equal to 23 cm or 9 inches. If the largest bamboo in Ecuador, Guadua angustifolia, had a circumference of at least three palms (0.69 m), which corresponds to a diameter of 0.22 m, the minimum height of this bamboo would be 0.69 multiplied by a constant value of 58.2, resulting in 40 meters. Comparing these dimensions to the current measurements of Guadua angustifolia, which have diameters of 0.10-0.12 m and heights of 18 to 21 m, we observe a reduction of approximately 50% in size over nearly 500 years.

Regarding the dimensions of the internodes, Simon (1637) mentioned that "The largest internodes have the capacity of one arroba of water." The arroba is a Spanish liquid measure equivalent to 25 pounds or 11,500 grams, which is equal to 11,500 cm3 of water capacity.

If the exterior diameter was 22 cm, the interior diameter would be approximately 18 cm. This suggests that the length of the internode was approximately 48-50 cm, likely measured from the center of the culm where the largest internodes are found.

Marco Polo, during his journey to India in 1290, reported seeing very large bamboos with a diameter of 45 cm, which the locals used as boats to navigate the largest rivers. He was likely referring to the species Dendrocalamus giganteus, the largest native bamboo in India. According to Prosea (1995), this bamboo now has a diameter of 18-25 cm and reaches heights of 26-30 meters. Consequently, this species has also experienced a reduction of approximately 50% in size over 730 years.

Based on the above evidence, it becomes evident that the diameter and height of bamboo culms in both Asia and the Americas have gradually decreased, possibly due to ongoing climatic changes worldwide and the destruction of bamboo forests over the past 200 years.