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IBM

MCP Math Server

by IBM

golden_ratio

Calculate the golden ratio φ (approximately 1.61803) for applications in mathematics, art, nature, and Fibonacci sequence analysis.

Instructions

Get the golden ratio φ ≈ 1.61803. Appears in art, nature, and Fibonacci sequence. (Domain: arithmetic, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It implies a read-only operation ('Get'), but does not disclose behavioral traits such as whether it's a constant lookup, if there are any side effects, or error conditions. The description adds some context about the golden ratio's applications, but lacks details on how the tool behaves beyond returning a value.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and front-loaded: the first sentence directly states the purpose. The additional context about where the golden ratio appears is relevant but could be more tightly integrated. It avoids unnecessary verbosity, making it efficient for an agent to parse.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is adequate but could be more complete. It explains what the tool returns but does not specify the format (e.g., numeric value, precision) or any limitations. For a constant-fetching tool, this is minimally viable but leaves room for improvement in clarifying output details.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The tool has 0 parameters, and the schema description coverage is 100% (since there are no parameters to describe). The description does not need to add parameter semantics, so it meets the baseline of 4 for tools with no parameters, as it doesn't have to compensate for any gaps.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Get the golden ratio φ ≈ 1.61803.' It specifies the verb ('Get') and resource ('golden ratio'), and provides the approximate value. However, it does not explicitly differentiate from sibling tools like 'compute_golden_ratio_continued_fraction' or 'compute_golden_ratio_fibonacci', which are also related to the golden ratio but compute it differently.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions that the golden ratio 'Appears in art, nature, and Fibonacci sequence,' which gives context but does not specify usage scenarios, prerequisites, or exclusions. With sibling tools that compute the golden ratio in various ways, this lack of differentiation is a significant gap.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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